CINXE.COM

<!DOCTYPE html> <html class="client-nojs vector-feature-language-in-header-enabled vector-feature-language-in-main-page-header-disabled vector-feature-sticky-header-disabled vector-feature-page-tools-pinned-disabled vector-feature-toc-pinned-clientpref-1 vector-feature-main-menu-pinned-disabled vector-feature-limited-width-clientpref-1 vector-feature-limited-width-content-enabled vector-feature-custom-font-size-clientpref-1 vector-feature-appearance-pinned-clientpref-1 vector-feature-night-mode-enabled skin-theme-clientpref-day vector-toc-available" lang="zh" dir="ltr"> <head> <meta charset="UTF-8"> <title>量子力学 - 维基百科，自由的百科全书</title> <script>(function(){var className="client-js vector-feature-language-in-header-enabled vector-feature-language-in-main-page-header-disabled vector-feature-sticky-header-disabled vector-feature-page-tools-pinned-disabled vector-feature-toc-pinned-clientpref-1 vector-feature-main-menu-pinned-disabled vector-feature-limited-width-clientpref-1 vector-feature-limited-width-content-enabled vector-feature-custom-font-size-clientpref-1 vector-feature-appearance-pinned-clientpref-1 vector-feature-night-mode-enabled skin-theme-clientpref-day vector-toc-available";var cookie=document.cookie.match(/(?:^|; )zhwikimwclientpreferences=([^;]+)/);if(cookie){cookie[1].split('%2C').forEach(function(pref){className=className.replace(new RegExp('(^| )'+pref.replace(/-clientpref-\w+$|[^\w-]+/g,'')+'-clientpref-\\w+( |$)'),'$1'+pref+'$2');});}document.documentElement.className=className;}());RLCONF={"wgBreakFrames":false,"wgSeparatorTransformTable":["",""],"wgDigitTransformTable":["",""],"wgDefaultDateFormat":"zh", "wgMonthNames":["","1月","2月","3月","4月","5月","6月","7月","8月","9月","10月","11月","12月"],"wgRequestId":"b88536cc-dcc6-4043-8c2f-5f1899ab2cb6","wgCanonicalNamespace":"","wgCanonicalSpecialPageName":false,"wgNamespaceNumber":0,"wgPageName":"量子力学","wgTitle":"量子力学","wgCurRevisionId":84856400,"wgRevisionId":84856400,"wgArticleId":6217,"wgIsArticle":true,"wgIsRedirect":false,"wgAction":"view","wgUserName":null,"wgUserGroups":["*"],"wgCategories":["含有过时参数的引用的页面","引文格式1维护：冗余文本","含有访问日期但无网址的引用的页面","引文格式1维护：显式使用等标签","引文格式1错误：日期","有单独入门介绍的条目","優良條目","含有英語的條目","需要查證來源的維基百科條目","使用的姊妹项目链接带有默认搜索的页面","包含FAST标识符的维基百科条目","包含BNE标识符的维基百科条目","包含BNF标识符的维基百科条目", "包含BNFdata标识符的维基百科条目","包含GND标识符的维基百科条目","包含J9U标识符的维基百科条目","包含LCCN标识符的维基百科条目","包含NDL标识符的维基百科条目","包含NKC标识符的维基百科条目","包含SUDOC标识符的维基百科条目","物理學中未解決的問題","量子力学"],"wgPageViewLanguage":"zh","wgPageContentLanguage":"zh","wgPageContentModel":"wikitext","wgRelevantPageName":"量子力学","wgRelevantArticleId":6217,"wgUserVariant":"zh","wgIsProbablyEditable":true,"wgRelevantPageIsProbablyEditable":true,"wgRestrictionEdit":[],"wgRestrictionMove":[],"wgRedirectedFrom":"量子物理學","wgNoticeProject":"wikipedia","wgCiteReferencePreviewsActive":true,"wgMediaViewerOnClick":true,"wgMediaViewerEnabledByDefault":true,"wgPopupsFlags":0,"wgVisualEditor":{"pageLanguageCode":"zh","pageLanguageDir":"ltr","pageVariantFallbacks":["zh-hans","zh-hant","zh-cn","zh-tw","zh-hk","zh-sg","zh-mo","zh-my"]}, "wgMFDisplayWikibaseDescriptions":{"search":true,"watchlist":true,"tagline":true,"nearby":true},"wgWMESchemaEditAttemptStepOversample":false,"wgWMEPageLength":70000,"wgInternalRedirectTargetUrl":"/wiki/%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6","wgRelatedArticlesCompat":[],"wgCentralAuthMobileDomain":false,"wgEditSubmitButtonLabelPublish":true,"wgULSPosition":"interlanguage","wgULSisCompactLinksEnabled":false,"wgVector2022LanguageInHeader":true,"wgULSisLanguageSelectorEmpty":false,"wgWikibaseItemId":"Q944","wgCheckUserClientHintsHeadersJsApi":["brands","architecture","bitness","fullVersionList","mobile","model","platform","platformVersion"],"GEHomepageSuggestedEditsEnableTopics":true,"wgGETopicsMatchModeEnabled":false,"wgGEStructuredTaskRejectionReasonTextInputEnabled":false,"wgGELevelingUpEnabledForUser":false};RLSTATE={"ext.gadget.large-font":"ready","ext.globalCssJs.user.styles":"ready","site.styles":"ready","user.styles":"ready","ext.globalCssJs.user":"ready","user":"ready", "user.options":"loading","ext.cite.styles":"ready","ext.math.styles":"ready","skins.vector.search.codex.styles":"ready","skins.vector.styles":"ready","skins.vector.icons":"ready","jquery.makeCollapsible.styles":"ready","ext.wikimediamessages.styles":"ready","ext.visualEditor.desktopArticleTarget.noscript":"ready","ext.uls.interlanguage":"ready","wikibase.client.init":"ready","ext.wikimediaBadges":"ready"};RLPAGEMODULES=["mediawiki.action.view.redirect","ext.cite.ux-enhancements","mediawiki.page.media","site","mediawiki.page.ready","jquery.makeCollapsible","mediawiki.toc","skins.vector.js","ext.centralNotice.geoIP","ext.centralNotice.startUp","ext.gadget.edit0","ext.gadget.WikiMiniAtlas","ext.gadget.UnihanTooltips","ext.gadget.Difflink","ext.gadget.pseudonamespace-UI","ext.gadget.SpecialWikitext","ext.gadget.switcher","ext.gadget.VariantAlly","ext.gadget.AdvancedSiteNotices","ext.gadget.hideConversionTab","ext.gadget.internalLinkHelper-altcolor","ext.gadget.noteTA","ext.gadget.NavFrame" ,"ext.gadget.collapsibleTables","ext.gadget.scrollUpButton","ext.urlShortener.toolbar","ext.centralauth.centralautologin","mmv.bootstrap","ext.popups","ext.visualEditor.desktopArticleTarget.init","ext.visualEditor.targetLoader","ext.echo.centralauth","ext.eventLogging","ext.wikimediaEvents","ext.navigationTiming","ext.uls.interface","ext.cx.eventlogging.campaigns","ext.cx.uls.quick.actions","wikibase.client.vector-2022","ext.checkUser.clientHints","ext.growthExperiments.SuggestedEditSession","wikibase.sidebar.tracking"];</script> <script>(RLQ=window.RLQ||[]).push(function(){mw.loader.impl(function(){return["user.options@12s5i",function($,jQuery,require,module){mw.user.tokens.set({"patrolToken":"+\\","watchToken":"+\\","csrfToken":"+\\"}); }];});});</script> <link rel="stylesheet" href="/w/load.php?lang=zh&modules=ext.cite.styles%7Cext.math.styles%7Cext.uls.interlanguage%7Cext.visualEditor.desktopArticleTarget.noscript%7Cext.wikimediaBadges%7Cext.wikimediamessages.styles%7Cjquery.makeCollapsible.styles%7Cskins.vector.icons%2Cstyles%7Cskins.vector.search.codex.styles%7Cwikibase.client.init&only=styles&skin=vector-2022"> <script async="" src="/w/load.php?lang=zh&modules=startup&only=scripts&raw=1&skin=vector-2022"></script> <meta name="ResourceLoaderDynamicStyles" content=""> <link rel="stylesheet" href="/w/load.php?lang=zh&modules=ext.gadget.large-font&only=styles&skin=vector-2022"> <link rel="stylesheet" href="/w/load.php?lang=zh&modules=site.styles&only=styles&skin=vector-2022"> <meta name="generator" content="MediaWiki 1.44.0-wmf.4"> <meta name="referrer" content="origin"> <meta name="referrer" content="origin-when-cross-origin"> <meta name="robots" content="max-image-preview:standard"> <meta name="format-detection" content="telephone=no"> <meta property="og:image" content="https://upload.wikimedia.org/wikipedia/commons/thumb/e/e7/Hydrogen_Density_Plots.png/1200px-Hydrogen_Density_Plots.png"> <meta property="og:image:width" content="1200"> <meta property="og:image:height" content="1091"> <meta property="og:image" content="https://upload.wikimedia.org/wikipedia/commons/thumb/e/e7/Hydrogen_Density_Plots.png/800px-Hydrogen_Density_Plots.png"> <meta property="og:image:width" content="800"> <meta property="og:image:height" content="727"> <meta property="og:image" content="https://upload.wikimedia.org/wikipedia/commons/thumb/e/e7/Hydrogen_Density_Plots.png/640px-Hydrogen_Density_Plots.png"> <meta property="og:image:width" content="640"> <meta property="og:image:height" content="582"> <meta name="viewport" content="width=1120"> <meta property="og:title" content="量子力学 - 维基百科，自由的百科全书"> <meta property="og:type" content="website"> <link rel="preconnect" href="//upload.wikimedia.org"> <link rel="alternate" media="only screen and (max-width: 640px)" href="//zh.m.wikipedia.org/wiki/%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6"> <link rel="alternate" type="application/x-wiki" title="编辑本页" href="/w/index.php?title=%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6&action=edit"> <link rel="apple-touch-icon" href="/static/apple-touch/wikipedia.png"> <link rel="icon" href="/static/favicon/wikipedia.ico"> <link rel="search" type="application/opensearchdescription+xml" href="/w/rest.php/v1/search" title="Wikipedia (zh)"> <link rel="EditURI" type="application/rsd+xml" href="//zh.wikipedia.org/w/api.php?action=rsd"> <link rel="canonical" href="https://zh.wikipedia.org/wiki/%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6"> <link rel="alternate" hreflang="zh" href="https://zh.wikipedia.org/wiki/%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6"> <link rel="alternate" hreflang="zh-Hans" href="https://zh.wikipedia.org/zh-hans/%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6"> <link rel="alternate" hreflang="zh-Hans-CN" href="https://zh.wikipedia.org/zh-cn/%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6"> <link rel="alternate" hreflang="zh-Hans-MY" href="https://zh.wikipedia.org/zh-my/%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6"> <link rel="alternate" hreflang="zh-Hans-SG" href="https://zh.wikipedia.org/zh-sg/%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6"> <link rel="alternate" hreflang="zh-Hant" href="https://zh.wikipedia.org/zh-hant/%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6"> <link rel="alternate" hreflang="zh-Hant-HK" href="https://zh.wikipedia.org/zh-hk/%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6"> <link rel="alternate" hreflang="zh-Hant-MO" href="https://zh.wikipedia.org/zh-mo/%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6"> <link rel="alternate" hreflang="zh-Hant-TW" href="https://zh.wikipedia.org/zh-tw/%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6"> <link rel="alternate" hreflang="x-default" href="https://zh.wikipedia.org/wiki/%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6"> <link rel="license" href="https://creativecommons.org/licenses/by-sa/4.0/deed.zh"> <link rel="alternate" type="application/atom+xml" title="Wikipedia的Atom feed" href="/w/index.php?title=Special:%E6%9C%80%E8%BF%91%E6%9B%B4%E6%94%B9&feed=atom"> <link rel="dns-prefetch" href="//meta.wikimedia.org" /> <link rel="dns-prefetch" href="//login.wikimedia.org"> </head> <body class="skin--responsive skin-vector skin-vector-search-vue mediawiki ltr sitedir-ltr mw-hide-empty-elt ns-0 ns-subject mw-editable page-量子力学 rootpage-量子力学 skin-vector-2022 action-view"><a class="mw-jump-link" href="#bodyContent">跳转到内容</a> <div class="vector-header-container"> <header class="vector-header mw-header"> <div class="vector-header-start"> <nav class="vector-main-menu-landmark" aria-label="站点"> <div id="vector-main-menu-dropdown" class="vector-dropdown vector-main-menu-dropdown vector-button-flush-left vector-button-flush-right" > <input type="checkbox" id="vector-main-menu-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-main-menu-dropdown" class="vector-dropdown-checkbox " aria-label="主菜单" > <label id="vector-main-menu-dropdown-label" for="vector-main-menu-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" > 主菜单 </label> <div class="vector-dropdown-content"> <div id="vector-main-menu-unpinned-container" class="vector-unpinned-container"> <div id="vector-main-menu" class="vector-main-menu vector-pinnable-element"> <div class="vector-pinnable-header vector-main-menu-pinnable-header vector-pinnable-header-unpinned" data-feature-name="main-menu-pinned" data-pinnable-element-id="vector-main-menu" data-pinned-container-id="vector-main-menu-pinned-container" data-unpinned-container-id="vector-main-menu-unpinned-container" > <div class="vector-pinnable-header-label">主菜单</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-main-menu.pin">移至侧栏</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-main-menu.unpin">隐藏</button> </div> <div id="p-navigation" class="vector-menu mw-portlet mw-portlet-navigation" > <div class="vector-menu-heading"> 导航 </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="n-mainpage-description" class="mw-list-item"><a href="/wiki/Wikipedia:%E9%A6%96%E9%A1%B5" title="访问首页[z]" accesskey="z">首页</a></li><li id="n-indexpage" class="mw-list-item"><a href="/wiki/Wikipedia:%E5%88%86%E7%B1%BB%E7%B4%A2%E5%BC%95" title="以分类索引搜寻中文维基百科">分类索引</a></li><li id="n-Featured_content" class="mw-list-item"><a href="/wiki/Portal:%E7%89%B9%E8%89%B2%E5%85%A7%E5%AE%B9" title="查看中文维基百科的特色内容">特色内容</a></li><li id="n-currentevents" class="mw-list-item"><a href="/wiki/Portal:%E6%96%B0%E8%81%9E%E5%8B%95%E6%85%8B" title="提供当前新闻事件的背景资料">新闻动态</a></li><li id="n-recentchanges" class="mw-list-item"><a href="/wiki/Special:%E6%9C%80%E8%BF%91%E6%9B%B4%E6%94%B9" title="列出维基百科中的最近修改[r]" accesskey="r">最近更改</a></li><li id="n-randompage" class="mw-list-item"><a href="/wiki/Special:%E9%9A%8F%E6%9C%BA%E9%A1%B5%E9%9D%A2" title="随机载入一个页面[x]" accesskey="x">随机条目</a></li> </ul> </div> </div> <div id="p-help" class="vector-menu mw-portlet mw-portlet-help" > <div class="vector-menu-heading"> 帮助 </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="n-help" class="mw-list-item"><a href="/wiki/Help:%E7%9B%AE%E5%BD%95" title="寻求帮助">帮助</a></li><li id="n-portal" class="mw-list-item"><a href="/wiki/Wikipedia:%E7%A4%BE%E7%BE%A4%E9%A6%96%E9%A1%B5" title="关于本计划、你可以做什么、应该如何做">维基社群</a></li><li id="n-policy" class="mw-list-item"><a href="/wiki/Wikipedia:%E6%96%B9%E9%87%9D%E8%88%87%E6%8C%87%E5%BC%95" title="查看维基百科的方针和指引">方针与指引</a></li><li id="n-villagepump" class="mw-list-item"><a href="/wiki/Wikipedia:%E4%BA%92%E5%8A%A9%E5%AE%A2%E6%A0%88" title="参与维基百科社群的讨论">互助客栈</a></li><li id="n-Information_desk" class="mw-list-item"><a href="/wiki/Wikipedia:%E7%9F%A5%E8%AF%86%E9%97%AE%E7%AD%94" title="解答任何与维基百科无关的问题的地方">知识问答</a></li><li id="n-conversion" class="mw-list-item"><a href="/wiki/Wikipedia:%E5%AD%97%E8%AF%8D%E8%BD%AC%E6%8D%A2" title="提出字词转换请求">字词转换</a></li><li id="n-IRC" class="mw-list-item"><a href="/wiki/Wikipedia:IRC%E8%81%8A%E5%A4%A9%E9%A2%91%E9%81%93">IRC即时聊天</a></li><li id="n-contact" class="mw-list-item"><a href="/wiki/Wikipedia:%E8%81%94%E7%BB%9C%E6%88%91%E4%BB%AC" title="如何联络维基百科">联络我们</a></li><li id="n-about" class="mw-list-item"><a href="/wiki/Wikipedia:%E5%85%B3%E4%BA%8E" title="查看维基百科的简介">关于维基百科</a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> <a href="/wiki/Wikipedia:%E9%A6%96%E9%A1%B5" class="mw-logo"> <img class="mw-logo-icon" src="/static/images/icons/wikipedia.png" alt="" aria-hidden="true" height="50" width="50"> <img class="mw-logo-wordmark" alt="维基百科" src="/static/images/mobile/copyright/wikipedia-wordmark-zh.svg" style="width: 6.5625em; height: 1.375em;"> <img class="mw-logo-tagline" alt="自由的百科全书" src="/static/images/mobile/copyright/wikipedia-tagline-zh.svg" width="103" height="14" style="width: 6.4375em; height: 0.875em;"> </a> </div> <div class="vector-header-end"> <div id="p-search" role="search" class="vector-search-box-vue vector-search-box-collapses vector-search-box-show-thumbnail vector-search-box-auto-expand-width vector-search-box"> <a href="/wiki/Special:%E6%90%9C%E7%B4%A2" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only search-toggle" title="搜索维基百科[f]" accesskey="f"> 搜索 </a> <div class="vector-typeahead-search-container"> <div class="cdx-typeahead-search cdx-typeahead-search--show-thumbnail cdx-typeahead-search--auto-expand-width"> <form action="/w/index.php" id="searchform" class="cdx-search-input cdx-search-input--has-end-button"> <div id="simpleSearch" class="cdx-search-input__input-wrapper" data-search-loc="header-moved"> <div class="cdx-text-input cdx-text-input--has-start-icon"> <input class="cdx-text-input__input" type="search" name="search" placeholder="搜索维基百科" aria-label="搜索维基百科" autocapitalize="sentences" title="搜索维基百科[f]" accesskey="f" id="searchInput" > </div> <input type="hidden" name="title" value="Special:搜索"> </div> <button class="cdx-button cdx-search-input__end-button">搜索</button> </form> </div> </div> </div> <nav class="vector-user-links vector-user-links-wide" aria-label="个人工具"> <div class="vector-user-links-main"> <div id="p-vector-user-menu-preferences" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <div id="p-vector-user-menu-userpage" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <nav class="vector-appearance-landmark" aria-label="外观"> <div id="vector-appearance-dropdown" class="vector-dropdown " title="更改页面字体大小、宽度和颜色的外观" > <input type="checkbox" id="vector-appearance-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-appearance-dropdown" class="vector-dropdown-checkbox " aria-label="外观" > <label id="vector-appearance-dropdown-label" for="vector-appearance-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" > 外观 </label> <div class="vector-dropdown-content"> <div id="vector-appearance-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <div id="p-vector-user-menu-notifications" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <div id="p-vector-user-menu-overflow" class="vector-menu mw-portlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="https://donate.wikimedia.org/?utm_source=donate&utm_medium=sidebar&utm_campaign=spontaneous&uselang=zh-hans" class="">资助维基百科</a> </li> <li id="pt-createaccount-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=Special:%E5%88%9B%E5%BB%BA%E8%B4%A6%E6%88%B7&returnto=%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6" title="我们推荐您创建账号并登录，但这不是强制性的" class="">创建账号</a> </li> <li id="pt-login-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=Special:%E7%94%A8%E6%88%B7%E7%99%BB%E5%BD%95&returnto=%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6" title="建议你登录，尽管并非必须。[o]" accesskey="o" class="">登录</a> </li> </ul> </div> </div> </div> <div id="vector-user-links-dropdown" class="vector-dropdown vector-user-menu vector-button-flush-right vector-user-menu-logged-out" title="更多选项" > <input type="checkbox" id="vector-user-links-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-user-links-dropdown" class="vector-dropdown-checkbox " aria-label="个人工具" > <label id="vector-user-links-dropdown-label" for="vector-user-links-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" > 个人工具 </label> <div class="vector-dropdown-content"> <div id="p-personal" class="vector-menu mw-portlet mw-portlet-personal user-links-collapsible-item" title="用户菜单" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport" class="user-links-collapsible-item mw-list-item"><a href="https://donate.wikimedia.org/?utm_source=donate&utm_medium=sidebar&utm_campaign=spontaneous&uselang=zh-hans">资助维基百科</a></li><li id="pt-createaccount" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Special:%E5%88%9B%E5%BB%BA%E8%B4%A6%E6%88%B7&returnto=%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6" title="我们推荐您创建账号并登录，但这不是强制性的"> 创建账号</a></li><li id="pt-login" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Special:%E7%94%A8%E6%88%B7%E7%99%BB%E5%BD%95&returnto=%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6" title="建议你登录，尽管并非必须。[o]" accesskey="o"> 登录</a></li> </ul> </div> </div> <div id="p-user-menu-anon-editor" class="vector-menu mw-portlet mw-portlet-user-menu-anon-editor" > <div class="vector-menu-heading"> 未登录编辑者的页面 <a href="/wiki/Help:%E6%96%B0%E6%89%8B%E5%85%A5%E9%97%A8" aria-label="了解有关编辑的更多信息">了解详情</a> </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-anoncontribs" class="mw-list-item"><a href="/wiki/Special:%E6%88%91%E7%9A%84%E8%B4%A1%E7%8C%AE" title="来自此IP地址的编辑列表[y]" accesskey="y">贡献</a></li><li id="pt-anontalk" class="mw-list-item"><a href="/wiki/Special:%E6%88%91%E7%9A%84%E8%AE%A8%E8%AE%BA%E9%A1%B5" title="对于来自此IP地址编辑的讨论[n]" accesskey="n">讨论</a></li> </ul> </div> </div> </div> </div> </nav> </div> </header> </div> <div class="mw-page-container"> <div class="mw-page-container-inner"> <div class="vector-sitenotice-container"> <div id="siteNotice"></div> </div> <div class="vector-column-start"> <div class="vector-main-menu-container"> <div id="mw-navigation"> <nav id="mw-panel" class="vector-main-menu-landmark" aria-label="站点"> <div id="vector-main-menu-pinned-container" class="vector-pinned-container"> </div> </nav> </div> </div> <div class="vector-sticky-pinned-container"> <nav id="mw-panel-toc" aria-label="目录" data-event-name="ui.sidebar-toc" class="mw-table-of-contents-container vector-toc-landmark"> <div id="vector-toc-pinned-container" class="vector-pinned-container"> <div id="vector-toc" class="vector-toc vector-pinnable-element"> <div class="vector-pinnable-header vector-toc-pinnable-header vector-pinnable-header-pinned" data-feature-name="toc-pinned" data-pinnable-element-id="vector-toc" > <h2 class="vector-pinnable-header-label">目录</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">移至侧栏</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">隐藏</button> </div> <ul class="vector-toc-contents" id="mw-panel-toc-list"> <li id="toc-mw-content-text" class="vector-toc-list-item vector-toc-level-1"> <a href="#" class="vector-toc-link"> <div class="vector-toc-text">序言</div> </a> </li> <li id="toc-关键现象、歷史背景" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#关键现象、歷史背景"> <div class="vector-toc-text"> 1 关键现象、歷史背景 </div> </a> <button aria-controls="toc-关键现象、歷史背景-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> 开关关键现象、歷史背景子章节 </button> <ul id="toc-关键现象、歷史背景-sublist" class="vector-toc-list"> <li id="toc-黑体辐射" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#黑体辐射"> <div class="vector-toc-text"> 1.1 黑体辐射 </div> </a> <ul id="toc-黑体辐射-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-光电效应" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#光电效应"> <div class="vector-toc-text"> 1.2 光电效应 </div> </a> <ul id="toc-光电效应-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-原子结构" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#原子结构"> <div class="vector-toc-text"> 1.3 原子结构 </div> </a> <ul id="toc-原子结构-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-物质波" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#物质波"> <div class="vector-toc-text"> 1.4 物质波 </div> </a> <ul id="toc-物质波-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-数学基础" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#数学基础"> <div class="vector-toc-text"> 2 数学基础 </div> </a> <button aria-controls="toc-数学基础-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> 开关数学基础子章节 </button> <ul id="toc-数学基础-sublist" class="vector-toc-list"> <li id="toc-基礎公設" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#基礎公設"> <div class="vector-toc-text"> 2.1 基礎公設 </div> </a> <ul id="toc-基礎公設-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-量子態與量子算符" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#量子態與量子算符"> <div class="vector-toc-text"> 2.2 量子態與量子算符 </div> </a> <ul id="toc-量子態與量子算符-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-动力学演化" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#动力学演化"> <div class="vector-toc-text"> 2.3 动力学演化 </div> </a> <ul id="toc-动力学演化-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-主要論題" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#主要論題"> <div class="vector-toc-text"> 3 主要論題 </div> </a> <button aria-controls="toc-主要論題-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> 开关主要論題子章节 </button> <ul id="toc-主要論題-sublist" class="vector-toc-list"> <li id="toc-测量过程" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#测量过程"> <div class="vector-toc-text"> 3.1 测量过程 </div> </a> <ul id="toc-测量过程-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-不确定性原理" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#不确定性原理"> <div class="vector-toc-text"> 3.2 不确定性原理 </div> </a> <ul id="toc-不确定性原理-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-全同粒子" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#全同粒子"> <div class="vector-toc-text"> 3.3 全同粒子 </div> </a> <ul id="toc-全同粒子-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-量子纠缠" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#量子纠缠"> <div class="vector-toc-text"> 3.4 量子纠缠 </div> </a> <ul id="toc-量子纠缠-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-量子退相干" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#量子退相干"> <div class="vector-toc-text"> 3.5 量子退相干 </div> </a> <ul id="toc-量子退相干-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-与其它物理理论的关系" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#与其它物理理论的关系"> <div class="vector-toc-text"> 4 与其它物理理论的关系 </div> </a> <button aria-controls="toc-与其它物理理论的关系-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> 开关与其它物理理论的关系子章节 </button> <ul id="toc-与其它物理理论的关系-sublist" class="vector-toc-list"> <li id="toc-經典物理" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#經典物理"> <div class="vector-toc-text"> 4.1 經典物理 </div> </a> <ul id="toc-經典物理-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-狹義相对论" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#狹義相对论"> <div class="vector-toc-text"> 4.2 狹義相对论 </div> </a> <ul id="toc-狹義相对论-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-粒子物理學" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#粒子物理學"> <div class="vector-toc-text"> 4.3 粒子物理學 </div> </a> <ul id="toc-粒子物理學-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-廣義相對論" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#廣義相對論"> <div class="vector-toc-text"> 4.4 廣義相對論 </div> </a> <ul id="toc-廣義相對論-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-哲学观点" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#哲学观点"> <div class="vector-toc-text"> 5 哲学观点 </div> </a> <ul id="toc-哲学观点-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-应用" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#应用"> <div class="vector-toc-text"> 6 应用 </div> </a> <button aria-controls="toc-应用-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> 开关应用子章节 </button> <ul id="toc-应用-sublist" class="vector-toc-list"> <li id="toc-电子器件" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#电子器件"> <div class="vector-toc-text"> 6.1 电子器件 </div> </a> <ul id="toc-电子器件-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-计算机" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#计算机"> <div class="vector-toc-text"> 6.2 计算机 </div> </a> <ul id="toc-计算机-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-宇宙學" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#宇宙學"> <div class="vector-toc-text"> 6.3 宇宙學 </div> </a> <ul id="toc-宇宙學-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-化学" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#化学"> <div class="vector-toc-text"> 6.4 化学 </div> </a> <ul id="toc-化学-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-信息学" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#信息学"> <div class="vector-toc-text"> 6.5 信息学 </div> </a> <ul id="toc-信息学-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-参见" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#参见"> <div class="vector-toc-text"> 7 参见 </div> </a> <ul id="toc-参见-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-註釋" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#註釋"> <div class="vector-toc-text"> 8 註釋 </div> </a> <ul id="toc-註釋-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-参考文献" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#参考文献"> <div class="vector-toc-text"> 9 参考文献 </div> </a> <ul id="toc-参考文献-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-外部链接" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#外部链接"> <div class="vector-toc-text"> 10 外部链接 </div> </a> <ul id="toc-外部链接-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="目录" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="开关目录" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" > 开关目录 </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading">量子力学</h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="前往另一种语言写成的文章。135种语言可用" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-135" aria-hidden="true" > 135种语言 </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-af mw-list-item"><a href="https://af.wikipedia.org/wiki/Kwantummeganika" title="Kwantummeganika – 南非荷兰语" lang="af" hreflang="af" data-title="Kwantummeganika" data-language-autonym="Afrikaans" data-language-local-name="南非荷兰语" class="interlanguage-link-target">Afrikaans</a></li><li class="interlanguage-link interwiki-als mw-list-item"><a href="https://als.wikipedia.org/wiki/Quantenmechanik" title="Quantenmechanik – 瑞士德语" lang="gsw" hreflang="gsw" data-title="Quantenmechanik" data-language-autonym="Alemannisch" data-language-local-name="瑞士德语" class="interlanguage-link-target">Alemannisch</a></li><li class="interlanguage-link interwiki-an mw-list-item"><a href="https://an.wikipedia.org/wiki/Mecanica_quantica" title="Mecanica quantica – 阿拉贡语" lang="an" hreflang="an" data-title="Mecanica quantica" data-language-autonym="Aragonés" data-language-local-name="阿拉贡语" class="interlanguage-link-target">Aragonés</a></li><li class="interlanguage-link interwiki-anp mw-list-item"><a href="https://anp.wikipedia.org/wiki/%E0%A4%95%E0%A5%8D%E0%A4%B5%E0%A4%BE%E0%A4%82%E0%A4%9F%E0%A4%AE_%E0%A4%B8%E0%A4%BF%E0%A4%A6%E0%A5%8D%E0%A4%A7%E0%A4%BE%E0%A4%82%E0%A4%A4" title="क्वांटम सिद्धांत – 昂加语" lang="anp" hreflang="anp" data-title="क्वांटम सिद्धांत" data-language-autonym="अंगिका" data-language-local-name="昂加语" class="interlanguage-link-target">अंगिका</a></li><li class="interlanguage-link interwiki-ar badge-Q17437798 badge-goodarticle mw-list-item" title="优良条目"><a href="https://ar.wikipedia.org/wiki/%D9%85%D9%8A%D9%83%D8%A7%D9%86%D9%8A%D9%83%D8%A7_%D8%A7%D9%84%D9%83%D9%85" title="ميكانيكا الكم – 阿拉伯语" lang="ar" hreflang="ar" data-title="ميكانيكا الكم" data-language-autonym="العربية" data-language-local-name="阿拉伯语" class="interlanguage-link-target">العربية</a></li><li class="interlanguage-link interwiki-arz mw-list-item"><a href="https://arz.wikipedia.org/wiki/%D8%A7%D9%84%D9%85%D9%8A%D9%83%D8%A7%D9%86%D9%8A%D9%83%D8%A7_%D8%A7%D9%84%D9%83%D9%85%D9%8A%D9%87" title="الميكانيكا الكميه – 埃及阿拉伯文" lang="arz" hreflang="arz" data-title="الميكانيكا الكميه" data-language-autonym="مصرى" data-language-local-name="埃及阿拉伯文" class="interlanguage-link-target">مصرى</a></li><li class="interlanguage-link interwiki-as mw-list-item"><a href="https://as.wikipedia.org/wiki/%E0%A6%95%E0%A7%8B%E0%A7%B1%E0%A6%BE%E0%A6%A3%E0%A7%8D%E0%A6%9F%E0%A6%BE%E0%A6%AE_%E0%A6%AC%E0%A6%B2%E0%A6%AC%E0%A6%BF%E0%A6%9C%E0%A7%8D%E0%A6%9E%E0%A6%BE%E0%A6%A8" title="কোৱাণ্টাম বলবিজ্ঞান – 阿萨姆语" lang="as" hreflang="as" data-title="কোৱাণ্টাম বলবিজ্ঞান" data-language-autonym="অসমীয়া" data-language-local-name="阿萨姆语" class="interlanguage-link-target">অসমীয়া</a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Mec%C3%A1nica_cu%C3%A1ntica" title="Mecánica cuántica – 阿斯图里亚斯语" lang="ast" hreflang="ast" data-title="Mecánica cuántica" data-language-autonym="Asturianu" data-language-local-name="阿斯图里亚斯语" class="interlanguage-link-target">Asturianu</a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Kvant_mexanikas%C4%B1" title="Kvant mexanikası – 阿塞拜疆语" lang="az" hreflang="az" data-title="Kvant mexanikası" data-language-autonym="Azərbaycanca" data-language-local-name="阿塞拜疆语" class="interlanguage-link-target">Azərbaycanca</a></li><li class="interlanguage-link interwiki-azb mw-list-item"><a href="https://azb.wikipedia.org/wiki/%DA%A9%D9%88%D8%A7%D9%86%D8%AA%D9%88%D9%85_%D9%85%DA%A9%D8%A7%D9%86%DB%8C%DA%A9%DB%8C" title="کوانتوم مکانیکی – South Azerbaijani" lang="azb" hreflang="azb" data-title="کوانتوم مکانیکی" data-language-autonym="تۆرکجه" data-language-local-name="South Azerbaijani" class="interlanguage-link-target">تۆرکجه</a></li><li class="interlanguage-link interwiki-ba mw-list-item"><a href="https://ba.wikipedia.org/wiki/%D0%9A%D0%B2%D0%B0%D0%BD%D1%82_%D0%BC%D0%B5%D1%85%D0%B0%D0%BD%D0%B8%D0%BA%D0%B0%D2%BB%D1%8B" title="Квант механикаһы – 巴什基尔语" lang="ba" hreflang="ba" data-title="Квант механикаһы" data-language-autonym="Башҡортса" data-language-local-name="巴什基尔语" class="interlanguage-link-target">Башҡортса</a></li><li class="interlanguage-link interwiki-ban mw-list-item"><a href="https://ban.wikipedia.org/wiki/M%C3%A9kanika_kuantum" title="Mékanika kuantum – 巴厘语" lang="ban" hreflang="ban" data-title="Mékanika kuantum" data-language-autonym="Basa Bali" data-language-local-name="巴厘语" class="interlanguage-link-target">Basa Bali</a></li><li class="interlanguage-link interwiki-bar mw-list-item"><a href="https://bar.wikipedia.org/wiki/Fuzalmechanik" title="Fuzalmechanik – 巴伐利亞文" lang="bar" hreflang="bar" data-title="Fuzalmechanik" data-language-autonym="Boarisch" data-language-local-name="巴伐利亞文" class="interlanguage-link-target">Boarisch</a></li><li class="interlanguage-link interwiki-bat-smg mw-list-item"><a href="https://bat-smg.wikipedia.org/wiki/Kvant%C4%97n%C4%97_mekan%C4%97ka" title="Kvantėnė mekanėka – 薩莫吉希亞文" lang="sgs" hreflang="sgs" data-title="Kvantėnė mekanėka" data-language-autonym="Žemaitėška" data-language-local-name="薩莫吉希亞文" class="interlanguage-link-target">Žemaitėška</a></li><li class="interlanguage-link interwiki-bcl mw-list-item"><a href="https://bcl.wikipedia.org/wiki/Mekanikang_kwantum" title="Mekanikang kwantum – Central Bikol" lang="bcl" hreflang="bcl" data-title="Mekanikang kwantum" data-language-autonym="Bikol Central" data-language-local-name="Central Bikol" class="interlanguage-link-target">Bikol Central</a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%9A%D0%B2%D0%B0%D0%BD%D1%82%D0%B0%D0%B2%D0%B0%D1%8F_%D0%BC%D0%B5%D1%85%D0%B0%D0%BD%D1%96%D0%BA%D0%B0" title="Квантавая механіка – 白俄罗斯语" lang="be" hreflang="be" data-title="Квантавая механіка" data-language-autonym="Беларуская" data-language-local-name="白俄罗斯语" class="interlanguage-link-target">Беларуская</a></li><li class="interlanguage-link interwiki-be-x-old mw-list-item"><a href="https://be-tarask.wikipedia.org/wiki/%D0%9A%D0%B2%D0%B0%D0%BD%D1%82%D0%B0%D0%B2%D0%B0%D1%8F_%D0%BC%D1%8D%D1%85%D0%B0%D0%BD%D1%96%D0%BA%D0%B0" title="Квантавая мэханіка – Belarusian (Taraškievica orthography)" lang="be-tarask" hreflang="be-tarask" data-title="Квантавая мэханіка" data-language-autonym="Беларуская (тарашкевіца)" data-language-local-name="Belarusian (Taraškievica orthography)" class="interlanguage-link-target">Беларуская (тарашкевіца)</a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%9A%D0%B2%D0%B0%D0%BD%D1%82%D0%BE%D0%B2%D0%B0_%D0%BC%D0%B5%D1%85%D0%B0%D0%BD%D0%B8%D0%BA%D0%B0" title="Квантова механика – 保加利亚语" lang="bg" hreflang="bg" data-title="Квантова механика" data-language-autonym="Български" data-language-local-name="保加利亚语" class="interlanguage-link-target">Български</a></li><li class="interlanguage-link interwiki-bh mw-list-item"><a href="https://bh.wikipedia.org/wiki/%E0%A4%95%E0%A5%8D%E0%A4%B5%E0%A4%BE%E0%A4%82%E0%A4%9F%E0%A4%AE_%E0%A4%AE%E0%A5%88%E0%A4%95%E0%A5%87%E0%A4%A8%E0%A4%BF%E0%A4%95%E0%A5%8D%E0%A4%B8" title="क्वांटम मैकेनिक्स – Bhojpuri" lang="bh" hreflang="bh" data-title="क्वांटम मैकेनिक्स" data-language-autonym="भोजपुरी" data-language-local-name="Bhojpuri" class="interlanguage-link-target">भोजपुरी</a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%95%E0%A7%8B%E0%A6%AF%E0%A6%BC%E0%A6%BE%E0%A6%A8%E0%A7%8D%E0%A6%9F%E0%A6%BE%E0%A6%AE_%E0%A6%AC%E0%A6%B2%E0%A6%AC%E0%A6%BF%E0%A6%9C%E0%A7%8D%E0%A6%9E%E0%A6%BE%E0%A6%A8" title="কোয়ান্টাম বলবিজ্ঞান – 孟加拉语" lang="bn" hreflang="bn" data-title="কোয়ান্টাম বলবিজ্ঞান" data-language-autonym="বাংলা" data-language-local-name="孟加拉语" class="interlanguage-link-target">বাংলা</a></li><li class="interlanguage-link interwiki-br mw-list-item"><a href="https://br.wikipedia.org/wiki/Mekanikerezh_kwantek" title="Mekanikerezh kwantek – 布列塔尼语" lang="br" hreflang="br" data-title="Mekanikerezh kwantek" data-language-autonym="Brezhoneg" data-language-local-name="布列塔尼语" class="interlanguage-link-target">Brezhoneg</a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Kvantna_mehanika" title="Kvantna mehanika – 波斯尼亚语" lang="bs" hreflang="bs" data-title="Kvantna mehanika" data-language-autonym="Bosanski" data-language-local-name="波斯尼亚语" class="interlanguage-link-target">Bosanski</a></li><li class="interlanguage-link interwiki-bxr mw-list-item"><a href="https://bxr.wikipedia.org/wiki/%D0%9A%D0%B2%D0%B0%D0%BD%D1%82%D1%8B%D0%BD_%D0%BC%D0%B5%D1%85%D0%B0%D0%BD%D0%B8%D0%BA%D0%B0" title="Квантын механика – Russia Buriat" lang="bxr" hreflang="bxr" data-title="Квантын механика" data-language-autonym="Буряад" data-language-local-name="Russia Buriat" class="interlanguage-link-target">Буряад</a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Mec%C3%A0nica_qu%C3%A0ntica" title="Mecànica quàntica – 加泰罗尼亚语" lang="ca" hreflang="ca" data-title="Mecànica quàntica" data-language-autonym="Català" data-language-local-name="加泰罗尼亚语" class="interlanguage-link-target">Català</a></li><li class="interlanguage-link interwiki-cdo mw-list-item"><a href="https://cdo.wikipedia.org/wiki/Li%C3%B4ng-c%E1%B9%B3%CC%84_l%C4%ADk-h%C5%8Fk" title="Liông-cṳ̄ lĭk-hŏk – Mindong" lang="cdo" hreflang="cdo" data-title="Liông-cṳ̄ lĭk-hŏk" data-language-autonym="閩東語 / Mìng-dĕ̤ng-ngṳ̄" data-language-local-name="Mindong" class="interlanguage-link-target">閩東語 / Mìng-dĕ̤ng-ngṳ̄</a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%D9%85%DB%8C%DA%A9%D8%A7%D9%86%DB%8C%DA%A9%DB%8C_%DA%A9%D9%88%D8%A7%D9%86%D8%AA%DB%86%D9%85" title="میکانیکی کوانتۆم – 中库尔德语" lang="ckb" hreflang="ckb" data-title="میکانیکی کوانتۆم" data-language-autonym="کوردی" data-language-local-name="中库尔德语" class="interlanguage-link-target">کوردی</a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Kvantov%C3%A1_mechanika" title="Kvantová mechanika – 捷克语" lang="cs" hreflang="cs" data-title="Kvantová mechanika" data-language-autonym="Čeština" data-language-local-name="捷克语" class="interlanguage-link-target">Čeština</a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%9A%D0%B2%D0%B0%D0%BD%D1%82%D0%BB%D0%B0_%D0%BC%D0%B5%D1%85%D0%B0%D0%BD%D0%B8%D0%BA%D0%B0" title="Квантла механика – 楚瓦什语" lang="cv" hreflang="cv" data-title="Квантла механика" data-language-autonym="Чӑвашла" data-language-local-name="楚瓦什语" class="interlanguage-link-target">Чӑвашла</a></li><li class="interlanguage-link interwiki-cy mw-list-item"><a href="https://cy.wikipedia.org/wiki/Mecaneg_cwantwm" title="Mecaneg cwantwm – 威尔士语" lang="cy" hreflang="cy" data-title="Mecaneg cwantwm" data-language-autonym="Cymraeg" data-language-local-name="威尔士语" class="interlanguage-link-target">Cymraeg</a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Kvantemekanik" title="Kvantemekanik – 丹麦语" lang="da" hreflang="da" data-title="Kvantemekanik" data-language-autonym="Dansk" data-language-local-name="丹麦语" class="interlanguage-link-target">Dansk</a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Quantenmechanik" title="Quantenmechanik – 德语" lang="de" hreflang="de" data-title="Quantenmechanik" data-language-autonym="Deutsch" data-language-local-name="德语" class="interlanguage-link-target">Deutsch</a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%9A%CE%B2%CE%B1%CE%BD%CF%84%CE%B9%CE%BA%CE%AE_%CE%BC%CE%B7%CF%87%CE%B1%CE%BD%CE%B9%CE%BA%CE%AE" title="Κβαντική μηχανική – 希腊语" lang="el" hreflang="el" data-title="Κβαντική μηχανική" data-language-autonym="Ελληνικά" data-language-local-name="希腊语" class="interlanguage-link-target">Ελληνικά</a></li><li class="interlanguage-link interwiki-en badge-Q17437798 badge-goodarticle mw-list-item" title="优良条目"><a href="https://en.wikipedia.org/wiki/Quantum_mechanics" title="Quantum mechanics – 英语" lang="en" hreflang="en" data-title="Quantum mechanics" data-language-autonym="English" data-language-local-name="英语" class="interlanguage-link-target">English</a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Kvantuma_mekaniko" title="Kvantuma mekaniko – 世界语" lang="eo" hreflang="eo" data-title="Kvantuma mekaniko" data-language-autonym="Esperanto" data-language-local-name="世界语" class="interlanguage-link-target">Esperanto</a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Mec%C3%A1nica_cu%C3%A1ntica" title="Mecánica cuántica – 西班牙语" lang="es" hreflang="es" data-title="Mecánica cuántica" data-language-autonym="Español" data-language-local-name="西班牙语" class="interlanguage-link-target">Español</a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Kvantmehaanika" title="Kvantmehaanika – 爱沙尼亚语" lang="et" hreflang="et" data-title="Kvantmehaanika" data-language-autonym="Eesti" data-language-local-name="爱沙尼亚语" class="interlanguage-link-target">Eesti</a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Mekanika_kuantiko" title="Mekanika kuantiko – 巴斯克语" lang="eu" hreflang="eu" data-title="Mekanika kuantiko" data-language-autonym="Euskara" data-language-local-name="巴斯克语" class="interlanguage-link-target">Euskara</a></li><li class="interlanguage-link interwiki-ext mw-list-item"><a href="https://ext.wikipedia.org/wiki/Mec%C3%A1nica_cu%C3%A1ntica" title="Mecánica cuántica – 埃斯特雷馬杜拉文" lang="ext" hreflang="ext" data-title="Mecánica cuántica" data-language-autonym="Estremeñu" data-language-local-name="埃斯特雷馬杜拉文" class="interlanguage-link-target">Estremeñu</a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D9%85%DA%A9%D8%A7%D9%86%DB%8C%DA%A9_%DA%A9%D9%88%D8%A7%D9%86%D8%AA%D9%88%D9%85%DB%8C" title="مکانیک کوانتومی – 波斯语" lang="fa" hreflang="fa" data-title="مکانیک کوانتومی" data-language-autonym="فارسی" data-language-local-name="波斯语" class="interlanguage-link-target">فارسی</a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Kvanttimekaniikka" title="Kvanttimekaniikka – 芬兰语" lang="fi" hreflang="fi" data-title="Kvanttimekaniikka" data-language-autonym="Suomi" data-language-local-name="芬兰语" class="interlanguage-link-target">Suomi</a></li><li class="interlanguage-link interwiki-fiu-vro mw-list-item"><a href="https://fiu-vro.wikipedia.org/wiki/Kvantmekaaniga" title="Kvantmekaaniga – 佛羅文" lang="vro" hreflang="vro" data-title="Kvantmekaaniga" data-language-autonym="Võro" data-language-local-name="佛羅文" class="interlanguage-link-target">Võro</a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/M%C3%A9canique_quantique" title="Mécanique quantique – 法语" lang="fr" hreflang="fr" data-title="Mécanique quantique" data-language-autonym="Français" data-language-local-name="法语" class="interlanguage-link-target">Français</a></li><li class="interlanguage-link interwiki-frr mw-list-item"><a href="https://frr.wikipedia.org/wiki/Kwantenmechaanik" title="Kwantenmechaanik – 北弗里西亚语" lang="frr" hreflang="frr" data-title="Kwantenmechaanik" data-language-autonym="Nordfriisk" data-language-local-name="北弗里西亚语" class="interlanguage-link-target">Nordfriisk</a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/Meicnic_chandamach" title="Meicnic chandamach – 爱尔兰语" lang="ga" hreflang="ga" data-title="Meicnic chandamach" data-language-autonym="Gaeilge" data-language-local-name="爱尔兰语" class="interlanguage-link-target">Gaeilge</a></li><li class="interlanguage-link interwiki-gcr mw-list-item"><a href="https://gcr.wikipedia.org/wiki/M%C3%A9kanik_kantik" title="Mékanik kantik – Guianan Creole" lang="gcr" hreflang="gcr" data-title="Mékanik kantik" data-language-autonym="Kriyòl gwiyannen" data-language-local-name="Guianan Creole" class="interlanguage-link-target">Kriyòl gwiyannen</a></li><li class="interlanguage-link interwiki-gd mw-list-item"><a href="https://gd.wikipedia.org/wiki/Meacanaigs_quantumach" title="Meacanaigs quantumach – 苏格兰盖尔语" lang="gd" hreflang="gd" data-title="Meacanaigs quantumach" data-language-autonym="Gàidhlig" data-language-local-name="苏格兰盖尔语" class="interlanguage-link-target">Gàidhlig</a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Mec%C3%A1nica_cu%C3%A1ntica" title="Mecánica cuántica – 加利西亚语" lang="gl" hreflang="gl" data-title="Mecánica cuántica" data-language-autonym="Galego" data-language-local-name="加利西亚语" class="interlanguage-link-target">Galego</a></li><li class="interlanguage-link interwiki-gn mw-list-item"><a href="https://gn.wikipedia.org/wiki/Mek%C3%A1nika_ku%C3%A1ntika" title="Mekánika kuántika – 瓜拉尼语" lang="gn" hreflang="gn" data-title="Mekánika kuántika" data-language-autonym="Avañe'ẽ" data-language-local-name="瓜拉尼语" class="interlanguage-link-target">Avañe'ẽ</a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%9E%D7%9B%D7%A0%D7%99%D7%A7%D7%AA_%D7%94%D7%A7%D7%95%D7%95%D7%A0%D7%98%D7%99%D7%9D" title="מכניקת הקוונטים – 希伯来语" lang="he" hreflang="he" data-title="מכניקת הקוונטים" data-language-autonym="עברית" data-language-local-name="希伯来语" class="interlanguage-link-target">עברית</a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%AA%E0%A5%8D%E0%A4%B0%E0%A4%AE%E0%A4%BE%E0%A4%A4%E0%A5%8D%E0%A4%B0%E0%A4%BE_%E0%A4%AF%E0%A4%BE%E0%A4%A8%E0%A5%8D%E0%A4%A4%E0%A5%8D%E0%A4%B0%E0%A4%BF%E0%A4%95%E0%A5%80" title="प्रमात्रा यान्त्रिकी – 印地语" lang="hi" hreflang="hi" data-title="प्रमात्रा यान्त्रिकी" data-language-autonym="हिन्दी" data-language-local-name="印地语" class="interlanguage-link-target">हिन्दी</a></li><li class="interlanguage-link interwiki-hif mw-list-item"><a href="https://hif.wikipedia.org/wiki/Quantum_mechanics" title="Quantum mechanics – 斐濟印地文" lang="hif" hreflang="hif" data-title="Quantum mechanics" data-language-autonym="Fiji Hindi" data-language-local-name="斐濟印地文" class="interlanguage-link-target">Fiji Hindi</a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Kvantna_mehanika" title="Kvantna mehanika – 克罗地亚语" lang="hr" hreflang="hr" data-title="Kvantna mehanika" data-language-autonym="Hrvatski" data-language-local-name="克罗地亚语" class="interlanguage-link-target">Hrvatski</a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Kvantummechanika" title="Kvantummechanika – 匈牙利语" lang="hu" hreflang="hu" data-title="Kvantummechanika" data-language-autonym="Magyar" data-language-local-name="匈牙利语" class="interlanguage-link-target">Magyar</a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D5%94%D5%BE%D5%A1%D5%B6%D5%BF%D5%A1%D5%B5%D5%AB%D5%B6_%D5%B4%D5%A5%D5%AD%D5%A1%D5%B6%D5%AB%D5%AF%D5%A1" title="Քվանտային մեխանիկա – 亚美尼亚语" lang="hy" hreflang="hy" data-title="Քվանտային մեխանիկա" data-language-autonym="Հայերեն" data-language-local-name="亚美尼亚语" class="interlanguage-link-target">Հայերեն</a></li><li class="interlanguage-link interwiki-hyw mw-list-item"><a href="https://hyw.wikipedia.org/wiki/%D5%94%D5%B8%D6%82%D5%A1%D5%B6%D5%BF%D5%A1%D5%B5%D5%AB%D5%B6_%D5%B4%D5%A5%D5%A3%D5%A1%D5%B6%D5%AB%D5%AF" title="Քուանտային մեգանիկ – Western Armenian" lang="hyw" hreflang="hyw" data-title="Քուանտային մեգանիկ" data-language-autonym="Արեւմտահայերէն" data-language-local-name="Western Armenian" class="interlanguage-link-target">Արեւմտահայերէն</a></li><li class="interlanguage-link interwiki-ia mw-list-item"><a href="https://ia.wikipedia.org/wiki/Mechanica_quantic" title="Mechanica quantic – 国际语" lang="ia" hreflang="ia" data-title="Mechanica quantic" data-language-autonym="Interlingua" data-language-local-name="国际语" class="interlanguage-link-target">Interlingua</a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Mekanika_kuantum" title="Mekanika kuantum – 印度尼西亚语" lang="id" hreflang="id" data-title="Mekanika kuantum" data-language-autonym="Bahasa Indonesia" data-language-local-name="印度尼西亚语" class="interlanguage-link-target">Bahasa Indonesia</a></li><li class="interlanguage-link interwiki-ig mw-list-item"><a href="https://ig.wikipedia.org/wiki/Quantum_mechanics" title="Quantum mechanics – 伊博语" lang="ig" hreflang="ig" data-title="Quantum mechanics" data-language-autonym="Igbo" data-language-local-name="伊博语" class="interlanguage-link-target">Igbo</a></li><li class="interlanguage-link interwiki-io mw-list-item"><a href="https://io.wikipedia.org/wiki/Quantumala_mekaniko" title="Quantumala mekaniko – 伊多语" lang="io" hreflang="io" data-title="Quantumala mekaniko" data-language-autonym="Ido" data-language-local-name="伊多语" class="interlanguage-link-target">Ido</a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/Skammtafr%C3%A6%C3%B0i" title="Skammtafræði – 冰岛语" lang="is" hreflang="is" data-title="Skammtafræði" data-language-autonym="Íslenska" data-language-local-name="冰岛语" class="interlanguage-link-target">Íslenska</a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Meccanica_quantistica" title="Meccanica quantistica – 意大利语" lang="it" hreflang="it" data-title="Meccanica quantistica" data-language-autonym="Italiano" data-language-local-name="意大利语" class="interlanguage-link-target">Italiano</a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6" title="量子力学 – 日语" lang="ja" hreflang="ja" data-title="量子力学" data-language-autonym="日本語" data-language-local-name="日语" class="interlanguage-link-target">日本語</a></li><li class="interlanguage-link interwiki-jam mw-list-item"><a href="https://jam.wikipedia.org/wiki/Kuantom_mikianix" title="Kuantom mikianix – 牙買加克里奧爾英文" lang="jam" hreflang="jam" data-title="Kuantom mikianix" data-language-autonym="Patois" data-language-local-name="牙買加克里奧爾英文" class="interlanguage-link-target">Patois</a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%99%E1%83%95%E1%83%90%E1%83%9C%E1%83%A2%E1%83%A3%E1%83%A0%E1%83%98_%E1%83%9B%E1%83%94%E1%83%A5%E1%83%90%E1%83%9C%E1%83%98%E1%83%99%E1%83%90" title="კვანტური მექანიკა – 格鲁吉亚语" lang="ka" hreflang="ka" data-title="კვანტური მექანიკა" data-language-autonym="ქართული" data-language-local-name="格鲁吉亚语" class="interlanguage-link-target">ქართული</a></li><li class="interlanguage-link interwiki-kaa mw-list-item"><a href="https://kaa.wikipedia.org/wiki/Kvant_mexanika" title="Kvant mexanika – 卡拉卡尔帕克语" lang="kaa" hreflang="kaa" data-title="Kvant mexanika" data-language-autonym="Qaraqalpaqsha" data-language-local-name="卡拉卡尔帕克语" class="interlanguage-link-target">Qaraqalpaqsha</a></li><li class="interlanguage-link interwiki-kbp mw-list-item"><a href="https://kbp.wikipedia.org/wiki/%C3%91%CA%8B%C5%8B_ho%C9%96e" title="Ñʋŋ hoɖe – Kabiye" lang="kbp" hreflang="kbp" data-title="Ñʋŋ hoɖe" data-language-autonym="Kabɩyɛ" data-language-local-name="Kabiye" class="interlanguage-link-target">Kabɩyɛ</a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%9A%D0%B2%D0%B0%D0%BD%D1%82%D1%82%D1%8B%D2%9B_%D0%BC%D0%B5%D1%85%D0%B0%D0%BD%D0%B8%D0%BA%D0%B0" title="Кванттық механика – 哈萨克语" lang="kk" hreflang="kk" data-title="Кванттық механика" data-language-autonym="Қазақша" data-language-local-name="哈萨克语" class="interlanguage-link-target">Қазақша</a></li><li class="interlanguage-link interwiki-kn mw-list-item"><a href="https://kn.wikipedia.org/wiki/%E0%B2%95%E0%B3%8D%E0%B2%B5%E0%B2%BE%E0%B2%82%E0%B2%9F%E0%B2%AE%E0%B3%8D_%E0%B2%AD%E0%B3%8C%E0%B2%A4%E0%B2%B6%E0%B2%BE%E0%B2%B8%E0%B3%8D%E0%B2%A4%E0%B3%8D%E0%B2%B0" title="ಕ್ವಾಂಟಮ್ ಭೌತಶಾಸ್ತ್ರ – 卡纳达语" lang="kn" hreflang="kn" data-title="ಕ್ವಾಂಟಮ್ ಭೌತಶಾಸ್ತ್ರ" data-language-autonym="ಕನ್ನಡ" data-language-local-name="卡纳达语" class="interlanguage-link-target">ಕನ್ನಡ</a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%96%91%EC%9E%90%EC%97%AD%ED%95%99" title="양자역학 – 韩语" lang="ko" hreflang="ko" data-title="양자역학" data-language-autonym="한국어" data-language-local-name="韩语" class="interlanguage-link-target">한국어</a></li><li class="interlanguage-link interwiki-ky mw-list-item"><a href="https://ky.wikipedia.org/wiki/%D0%9A%D0%B2%D0%B0%D0%BD%D1%82%D1%82%D1%8B%D0%BA_%D0%BC%D0%B5%D1%85%D0%B0%D0%BD%D0%B8%D0%BA%D0%B0" title="Кванттык механика – 柯尔克孜语" lang="ky" hreflang="ky" data-title="Кванттык механика" data-language-autonym="Кыргызча" data-language-local-name="柯尔克孜语" class="interlanguage-link-target">Кыргызча</a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Mechanica_quantica" title="Mechanica quantica – 拉丁语" lang="la" hreflang="la" data-title="Mechanica quantica" data-language-autonym="Latina" data-language-local-name="拉丁语" class="interlanguage-link-target">Latina</a></li><li class="interlanguage-link interwiki-li mw-list-item"><a href="https://li.wikipedia.org/wiki/Kwantummechanica" title="Kwantummechanica – 林堡语" lang="li" hreflang="li" data-title="Kwantummechanica" data-language-autonym="Limburgs" data-language-local-name="林堡语" class="interlanguage-link-target">Limburgs</a></li><li class="interlanguage-link interwiki-lmo mw-list-item"><a href="https://lmo.wikipedia.org/wiki/Mec%C3%A0nega_quant%C3%ACstega" title="Mecànega quantìstega – 倫巴底文" lang="lmo" hreflang="lmo" data-title="Mecànega quantìstega" data-language-autonym="Lombard" data-language-local-name="倫巴底文" class="interlanguage-link-target">Lombard</a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Kvantin%C4%97_mechanika" title="Kvantinė mechanika – 立陶宛语" lang="lt" hreflang="lt" data-title="Kvantinė mechanika" data-language-autonym="Lietuvių" data-language-local-name="立陶宛语" class="interlanguage-link-target">Lietuvių</a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Kvantu_meh%C4%81nika" title="Kvantu mehānika – 拉脱维亚语" lang="lv" hreflang="lv" data-title="Kvantu mehānika" data-language-autonym="Latviešu" data-language-local-name="拉脱维亚语" class="interlanguage-link-target">Latviešu</a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%9A%D0%B2%D0%B0%D0%BD%D1%82%D0%BD%D0%B0_%D0%BC%D0%B5%D1%85%D0%B0%D0%BD%D0%B8%D0%BA%D0%B0" title="Квантна механика – 马其顿语" lang="mk" hreflang="mk" data-title="Квантна механика" data-language-autonym="Македонски" data-language-local-name="马其顿语" class="interlanguage-link-target">Македонски</a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%95%E0%B5%8D%E0%B4%B5%E0%B4%BE%E0%B4%A3%E0%B5%8D%E0%B4%9F%E0%B4%82_%E0%B4%AC%E0%B4%B2%E0%B4%A4%E0%B4%A8%E0%B5%8D%E0%B4%A4%E0%B5%8D%E0%B4%B0%E0%B4%82" title="ക്വാണ്ടം ബലതന്ത്രം – 马拉雅拉姆语" lang="ml" hreflang="ml" data-title="ക്വാണ്ടം ബലതന്ത്രം" data-language-autonym="മലയാളം" data-language-local-name="马拉雅拉姆语" class="interlanguage-link-target">മലയാളം</a></li><li class="interlanguage-link interwiki-mn mw-list-item"><a href="https://mn.wikipedia.org/wiki/%D0%9A%D0%B2%D0%B0%D0%BD%D1%82_%D0%BC%D0%B5%D1%85%D0%B0%D0%BD%D0%B8%D0%BA" title="Квант механик – 蒙古语" lang="mn" hreflang="mn" data-title="Квант механик" data-language-autonym="Монгол" data-language-local-name="蒙古语" class="interlanguage-link-target">Монгол</a></li><li class="interlanguage-link interwiki-mr mw-list-item"><a href="https://mr.wikipedia.org/wiki/%E0%A4%AA%E0%A5%81%E0%A4%82%E0%A4%9C_%E0%A4%AF%E0%A4%BE%E0%A4%AE%E0%A4%BF%E0%A4%95%E0%A5%80" title="पुंज यामिकी – 马拉地语" lang="mr" hreflang="mr" data-title="पुंज यामिकी" data-language-autonym="मराठी" data-language-local-name="马拉地语" class="interlanguage-link-target">मराठी</a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Mekanik_kuantum" title="Mekanik kuantum – 马来语" lang="ms" hreflang="ms" data-title="Mekanik kuantum" data-language-autonym="Bahasa Melayu" data-language-local-name="马来语" class="interlanguage-link-target">Bahasa Melayu</a></li><li class="interlanguage-link interwiki-mt mw-list-item"><a href="https://mt.wikipedia.org/wiki/Mekkanika_kwantistika" title="Mekkanika kwantistika – 马耳他语" lang="mt" hreflang="mt" data-title="Mekkanika kwantistika" data-language-autonym="Malti" data-language-local-name="马耳他语" class="interlanguage-link-target">Malti</a></li><li class="interlanguage-link interwiki-my mw-list-item"><a href="https://my.wikipedia.org/wiki/%E1%80%80%E1%80%BD%E1%80%99%E1%80%BA%E1%80%90%E1%80%99%E1%80%BA%E1%80%99%E1%80%80%E1%80%B9%E1%80%80%E1%80%84%E1%80%BA%E1%80%B8%E1%80%94%E1%80%85%E1%80%BA" title="ကွမ်တမ်မက္ကင်းနစ် – 缅甸语" lang="my" hreflang="my" data-title="ကွမ်တမ်မက္ကင်းနစ်" data-language-autonym="မြန်မာဘာသာ" data-language-local-name="缅甸语" class="interlanguage-link-target">မြန်မာဘာသာ</a></li><li class="interlanguage-link interwiki-mzn mw-list-item"><a href="https://mzn.wikipedia.org/wiki/%DA%A9%D9%88%D8%A7%D9%86%D8%AA%D9%88%D9%85%DB%8C_%D9%81%DB%8C%D8%B2%DB%8C%DA%A9" title="کوانتومی فیزیک – 马赞德兰语" lang="mzn" hreflang="mzn" data-title="کوانتومی فیزیک" data-language-autonym="مازِرونی" data-language-local-name="马赞德兰语" class="interlanguage-link-target">مازِرونی</a></li><li class="interlanguage-link interwiki-nds mw-list-item"><a href="https://nds.wikipedia.org/wiki/Quantenmechanik" title="Quantenmechanik – 低地德语" lang="nds" hreflang="nds" data-title="Quantenmechanik" data-language-autonym="Plattdüütsch" data-language-local-name="低地德语" class="interlanguage-link-target">Plattdüütsch</a></li><li class="interlanguage-link interwiki-ne mw-list-item"><a href="https://ne.wikipedia.org/wiki/%E0%A4%AA%E0%A5%8D%E0%A4%B0%E0%A4%AE%E0%A4%BE%E0%A4%A4%E0%A5%8D%E0%A4%B0%E0%A4%BE_%E0%A4%AF%E0%A4%BE%E0%A4%A8%E0%A5%8D%E0%A4%A4%E0%A5%8D%E0%A4%B0%E0%A4%BF%E0%A4%95%E0%A5%80" title="प्रमात्रा यान्त्रिकी – 尼泊尔语" lang="ne" hreflang="ne" data-title="प्रमात्रा यान्त्रिकी" data-language-autonym="नेपाली" data-language-local-name="尼泊尔语" class="interlanguage-link-target">नेपाली</a></li><li class="interlanguage-link interwiki-new mw-list-item"><a href="https://new.wikipedia.org/wiki/%E0%A4%95%E0%A5%8D%E0%A4%B5%E0%A4%BE%E0%A4%A8%E0%A5%8D%E0%A4%9F%E0%A4%AE_%E0%A4%AE%E0%A5%87%E0%A4%95%E0%A4%BE%E0%A4%A8%E0%A4%BF%E0%A4%95%E0%A5%8D%E0%A4%B8%E0%A5%8D" title="क्वान्टम मेकानिक्स् – 尼瓦尔语" lang="new" hreflang="new" data-title="क्वान्टम मेकानिक्स्" data-language-autonym="नेपाल भाषा" data-language-local-name="尼瓦尔语" class="interlanguage-link-target">नेपाल भाषा</a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Kwantummechanica" title="Kwantummechanica – 荷兰语" lang="nl" hreflang="nl" data-title="Kwantummechanica" data-language-autonym="Nederlands" data-language-local-name="荷兰语" class="interlanguage-link-target">Nederlands</a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Kvantemekanikk" title="Kvantemekanikk – 挪威尼诺斯克语" lang="nn" hreflang="nn" data-title="Kvantemekanikk" data-language-autonym="Norsk nynorsk" data-language-local-name="挪威尼诺斯克语" class="interlanguage-link-target">Norsk nynorsk</a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Kvantemekanikk" title="Kvantemekanikk – 书面挪威语" lang="nb" hreflang="nb" data-title="Kvantemekanikk" data-language-autonym="Norsk bokmål" data-language-local-name="书面挪威语" class="interlanguage-link-target">Norsk bokmål</a></li><li class="interlanguage-link interwiki-oc mw-list-item"><a href="https://oc.wikipedia.org/wiki/Mecanica_quantica" title="Mecanica quantica – 奥克语" lang="oc" hreflang="oc" data-title="Mecanica quantica" data-language-autonym="Occitan" data-language-local-name="奥克语" class="interlanguage-link-target">Occitan</a></li><li class="interlanguage-link interwiki-pa mw-list-item"><a href="https://pa.wikipedia.org/wiki/%E0%A8%95%E0%A9%81%E0%A8%86%E0%A8%82%E0%A8%9F%E0%A8%AE_%E0%A8%AE%E0%A8%95%E0%A9%88%E0%A8%A8%E0%A8%BF%E0%A8%95%E0%A8%B8" title="ਕੁਆਂਟਮ ਮਕੈਨਿਕਸ – 旁遮普语" lang="pa" hreflang="pa" data-title="ਕੁਆਂਟਮ ਮਕੈਨਿਕਸ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="旁遮普语" class="interlanguage-link-target">ਪੰਜਾਬੀ</a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Mechanika_kwantowa" title="Mechanika kwantowa – 波兰语" lang="pl" hreflang="pl" data-title="Mechanika kwantowa" data-language-autonym="Polski" data-language-local-name="波兰语" class="interlanguage-link-target">Polski</a></li><li class="interlanguage-link interwiki-pms mw-list-item"><a href="https://pms.wikipedia.org/wiki/Mec%C3%A0nica_qu%C3%A0ntica" title="Mecànica quàntica – 皮埃蒙特文" lang="pms" hreflang="pms" data-title="Mecànica quàntica" data-language-autonym="Piemontèis" data-language-local-name="皮埃蒙特文" class="interlanguage-link-target">Piemontèis</a></li><li class="interlanguage-link interwiki-pnb mw-list-item"><a href="https://pnb.wikipedia.org/wiki/%DA%A9%D9%88%D8%A7%D9%86%D9%B9%D9%85_%D9%85%DA%A9%DB%8C%D9%86%DA%A9%D8%B3" title="کوانٹم مکینکس – Western Punjabi" lang="pnb" hreflang="pnb" data-title="کوانٹم مکینکس" data-language-autonym="پنجابی" data-language-local-name="Western Punjabi" class="interlanguage-link-target">پنجابی</a></li><li class="interlanguage-link interwiki-ps mw-list-item"><a href="https://ps.wikipedia.org/wiki/%DA%A9%D9%88%D8%A7%D9%86%D9%BC%D9%88%D9%85_%D9%85%DB%8C%D8%AE%D8%A7%D9%86%DB%8C%DA%A9" title="کوانټوم میخانیک – 普什图语" lang="ps" hreflang="ps" data-title="کوانټوم میخانیک" data-language-autonym="پښتو" data-language-local-name="普什图语" class="interlanguage-link-target">پښتو</a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Mec%C3%A2nica_qu%C3%A2ntica" title="Mecânica quântica – 葡萄牙语" lang="pt" hreflang="pt" data-title="Mecânica quântica" data-language-autonym="Português" data-language-local-name="葡萄牙语" class="interlanguage-link-target">Português</a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Mecanic%C4%83_cuantic%C4%83" title="Mecanică cuantică – 罗马尼亚语" lang="ro" hreflang="ro" data-title="Mecanică cuantică" data-language-autonym="Română" data-language-local-name="罗马尼亚语" class="interlanguage-link-target">Română</a></li><li class="interlanguage-link interwiki-ru badge-Q17437798 badge-goodarticle mw-list-item" title="优良条目"><a href="https://ru.wikipedia.org/wiki/%D0%9A%D0%B2%D0%B0%D0%BD%D1%82%D0%BE%D0%B2%D0%B0%D1%8F_%D0%BC%D0%B5%D1%85%D0%B0%D0%BD%D0%B8%D0%BA%D0%B0" title="Квантовая механика – 俄语" lang="ru" hreflang="ru" data-title="Квантовая механика" data-language-autonym="Русский" data-language-local-name="俄语" class="interlanguage-link-target">Русский</a></li><li class="interlanguage-link interwiki-rue mw-list-item"><a href="https://rue.wikipedia.org/wiki/%D0%9A%D0%B2%D0%B0%D0%BD%D1%82%D0%BE%D0%B2%D0%B0_%D0%BC%D0%B5%D1%85%D0%B0%D0%BD%D1%96%D0%BA%D0%B0" title="Квантова механіка – 盧森尼亞文" lang="rue" hreflang="rue" data-title="Квантова механіка" data-language-autonym="Русиньскый" data-language-local-name="盧森尼亞文" class="interlanguage-link-target">Русиньскый</a></li><li class="interlanguage-link interwiki-sah mw-list-item"><a href="https://sah.wikipedia.org/wiki/%D0%9A%D0%B2%D0%B0%D0%BD%D1%82%D0%BE%D0%B2%D0%B0%D0%B9_%D1%84%D0%B8%D0%B7%D0%B8%D0%BA%D0%B0" title="Квантовай физика – 萨哈语" lang="sah" hreflang="sah" data-title="Квантовай физика" data-language-autonym="Саха тыла" data-language-local-name="萨哈语" class="interlanguage-link-target">Саха тыла</a></li><li class="interlanguage-link interwiki-scn mw-list-item"><a href="https://scn.wikipedia.org/wiki/Micc%C3%A0nica_quant%C3%ACstica" title="Miccànica quantìstica – 西西里语" lang="scn" hreflang="scn" data-title="Miccànica quantìstica" data-language-autonym="Sicilianu" data-language-local-name="西西里语" class="interlanguage-link-target">Sicilianu</a></li><li class="interlanguage-link interwiki-sco mw-list-item"><a href="https://sco.wikipedia.org/wiki/Quantum_mechanics" title="Quantum mechanics – 苏格兰语" lang="sco" hreflang="sco" data-title="Quantum mechanics" data-language-autonym="Scots" data-language-local-name="苏格兰语" class="interlanguage-link-target">Scots</a></li><li class="interlanguage-link interwiki-sd mw-list-item"><a href="https://sd.wikipedia.org/wiki/%DA%AA%D9%88%D8%A7%D9%86%D9%BD%D9%85_%D9%85%DA%AA%D9%8A%D9%86%DA%AA%D8%B3" title="ڪوانٽم مڪينڪس – 信德语" lang="sd" hreflang="sd" data-title="ڪوانٽم مڪينڪس" data-language-autonym="سنڌي" data-language-local-name="信德语" class="interlanguage-link-target">سنڌي</a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Kvantna_mehanika" title="Kvantna mehanika – 塞尔维亚-克罗地亚语" lang="sh" hreflang="sh" data-title="Kvantna mehanika" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="塞尔维亚-克罗地亚语" class="interlanguage-link-target">Srpskohrvatski / српскохрватски</a></li><li class="interlanguage-link interwiki-shi mw-list-item"><a href="https://shi.wikipedia.org/wiki/Tamikanikt_tasmktant" title="Tamikanikt tasmktant – 希尔哈语" lang="shi" hreflang="shi" data-title="Tamikanikt tasmktant" data-language-autonym="Taclḥit" data-language-local-name="希尔哈语" class="interlanguage-link-target">Taclḥit</a></li><li class="interlanguage-link interwiki-si mw-list-item"><a href="https://si.wikipedia.org/wiki/%E0%B6%9A%E0%B7%8A%E0%B7%80%E0%B7%9C%E0%B6%B1%E0%B7%8A%E0%B6%A7%E0%B6%B8%E0%B7%8A_%E0%B6%BA%E0%B7%8F%E0%B6%B1%E0%B7%8A%E0%B6%AD%E0%B7%8A%E2%80%8D%E0%B6%BB_%E0%B7%80%E0%B7%92%E0%B6%AF%E0%B7%8A%E2%80%8D%E0%B6%BA%E0%B7%8F%E2%80%8D%E0%B7%80" title="ක්වොන්ටම් යාන්ත්‍ර විද්‍යා‍ව – 僧伽罗语" lang="si" hreflang="si" data-title="ක්වොන්ටම් යාන්ත්‍ර විද්‍යා‍ව" data-language-autonym="සිංහල" data-language-local-name="僧伽罗语" class="interlanguage-link-target">සිංහල</a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Quantum_mechanics" title="Quantum mechanics – Simple English" lang="en-simple" hreflang="en-simple" data-title="Quantum mechanics" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target">Simple English</a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Kvantov%C3%A1_mechanika" title="Kvantová mechanika – 斯洛伐克语" lang="sk" hreflang="sk" data-title="Kvantová mechanika" data-language-autonym="Slovenčina" data-language-local-name="斯洛伐克语" class="interlanguage-link-target">Slovenčina</a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Kvantna_mehanika" title="Kvantna mehanika – 斯洛文尼亚语" lang="sl" hreflang="sl" data-title="Kvantna mehanika" data-language-autonym="Slovenščina" data-language-local-name="斯洛文尼亚语" class="interlanguage-link-target">Slovenščina</a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Mekanika_kuantike" title="Mekanika kuantike – 阿尔巴尼亚语" lang="sq" hreflang="sq" data-title="Mekanika kuantike" data-language-autonym="Shqip" data-language-local-name="阿尔巴尼亚语" class="interlanguage-link-target">Shqip</a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%9A%D0%B2%D0%B0%D0%BD%D1%82%D0%BD%D0%B0_%D0%BC%D0%B5%D1%85%D0%B0%D0%BD%D0%B8%D0%BA%D0%B0" title="Квантна механика – 塞尔维亚语" lang="sr" hreflang="sr" data-title="Квантна механика" data-language-autonym="Српски / srpski" data-language-local-name="塞尔维亚语" class="interlanguage-link-target">Српски / srpski</a></li><li class="interlanguage-link interwiki-su mw-list-item"><a href="https://su.wikipedia.org/wiki/M%C3%A9kanika_kuantum" title="Mékanika kuantum – 巽他语" lang="su" hreflang="su" data-title="Mékanika kuantum" data-language-autonym="Sunda" data-language-local-name="巽他语" class="interlanguage-link-target">Sunda</a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Kvantmekanik" title="Kvantmekanik – 瑞典语" lang="sv" hreflang="sv" data-title="Kvantmekanik" data-language-autonym="Svenska" data-language-local-name="瑞典语" class="interlanguage-link-target">Svenska</a></li><li class="interlanguage-link interwiki-sw mw-list-item"><a href="https://sw.wikipedia.org/wiki/Umakanika_kwanta" title="Umakanika kwanta – 斯瓦希里语" lang="sw" hreflang="sw" data-title="Umakanika kwanta" data-language-autonym="Kiswahili" data-language-local-name="斯瓦希里语" class="interlanguage-link-target">Kiswahili</a></li><li class="interlanguage-link interwiki-szl mw-list-item"><a href="https://szl.wikipedia.org/wiki/Kwantow%C5%8F_mechanika" title="Kwantowŏ mechanika – 西里西亚语" lang="szl" hreflang="szl" data-title="Kwantowŏ mechanika" data-language-autonym="Ślůnski" data-language-local-name="西里西亚语" class="interlanguage-link-target">Ślůnski</a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%95%E0%AF%81%E0%AE%B5%E0%AE%BE%E0%AE%A3%E0%AF%8D%E0%AE%9F%E0%AE%AE%E0%AF%8D_%E0%AE%87%E0%AE%AF%E0%AE%99%E0%AF%8D%E0%AE%95%E0%AE%BF%E0%AE%AF%E0%AE%B2%E0%AF%8D" title="குவாண்டம் இயங்கியல் – 泰米尔语" lang="ta" hreflang="ta" data-title="குவாண்டம் இயங்கியல்" data-language-autonym="தமிழ்" data-language-local-name="泰米尔语" class="interlanguage-link-target">தமிழ்</a></li><li class="interlanguage-link interwiki-te mw-list-item"><a href="https://te.wikipedia.org/wiki/%E0%B0%95%E0%B1%8D%E0%B0%B5%E0%B0%BE%E0%B0%82%E0%B0%9F%E0%B0%82_%E0%B0%AF%E0%B0%BE%E0%B0%82%E0%B0%A4%E0%B1%8D%E0%B0%B0%E0%B0%BF%E0%B0%95_%E0%B0%B6%E0%B0%BE%E0%B0%B8%E0%B1%8D%E0%B0%A4%E0%B1%8D%E0%B0%B0%E0%B0%82" title="క్వాంటం యాంత్రిక శాస్త్రం – 泰卢固语" lang="te" hreflang="te" data-title="క్వాంటం యాంత్రిక శాస్త్రం" data-language-autonym="తెలుగు" data-language-local-name="泰卢固语" class="interlanguage-link-target">తెలుగు</a></li><li class="interlanguage-link interwiki-tg mw-list-item"><a href="https://tg.wikipedia.org/wiki/%D0%9C%D0%B5%D1%85%D0%B0%D0%BD%D0%B8%D0%BA%D0%B0%D0%B8_%D0%BA%D0%B2%D0%B0%D0%BD%D1%82%D3%A3" title="Механикаи квантӣ – 塔吉克语" lang="tg" hreflang="tg" data-title="Механикаи квантӣ" data-language-autonym="Тоҷикӣ" data-language-local-name="塔吉克语" class="interlanguage-link-target">Тоҷикӣ</a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%81%E0%B8%A5%E0%B8%A8%E0%B8%B2%E0%B8%AA%E0%B8%95%E0%B8%A3%E0%B9%8C%E0%B8%84%E0%B8%A7%E0%B8%AD%E0%B8%99%E0%B8%95%E0%B8%B1%E0%B8%A1" title="กลศาสตร์ควอนตัม – 泰语" lang="th" hreflang="th" data-title="กลศาสตร์ควอนตัม" data-language-autonym="ไทย" data-language-local-name="泰语" class="interlanguage-link-target">ไทย</a></li><li class="interlanguage-link interwiki-tl mw-list-item"><a href="https://tl.wikipedia.org/wiki/Mekanikang_quantum" title="Mekanikang quantum – 他加禄语" lang="tl" hreflang="tl" data-title="Mekanikang quantum" data-language-autonym="Tagalog" data-language-local-name="他加禄语" class="interlanguage-link-target">Tagalog</a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Kuantum_mekani%C4%9Fi" title="Kuantum mekaniği – 土耳其语" lang="tr" hreflang="tr" data-title="Kuantum mekaniği" data-language-autonym="Türkçe" data-language-local-name="土耳其语" class="interlanguage-link-target">Türkçe</a></li><li class="interlanguage-link interwiki-tt mw-list-item"><a href="https://tt.wikipedia.org/wiki/%D0%9A%D0%B2%D0%B0%D0%BD%D1%82_%D0%BC%D0%B5%D1%85%D0%B0%D0%BD%D0%B8%D0%BA%D0%B0%D1%81%D1%8B" title="Квант механикасы – 鞑靼语" lang="tt" hreflang="tt" data-title="Квант механикасы" data-language-autonym="Татарча / tatarça" data-language-local-name="鞑靼语" class="interlanguage-link-target">Татарча / tatarça</a></li><li class="interlanguage-link interwiki-uk badge-Q17437796 badge-featuredarticle mw-list-item" title="典范条目"><a href="https://uk.wikipedia.org/wiki/%D0%9A%D0%B2%D0%B0%D0%BD%D1%82%D0%BE%D0%B2%D0%B0_%D0%BC%D0%B5%D1%85%D0%B0%D0%BD%D1%96%D0%BA%D0%B0" title="Квантова механіка – 乌克兰语" lang="uk" hreflang="uk" data-title="Квантова механіка" data-language-autonym="Українська" data-language-local-name="乌克兰语" class="interlanguage-link-target">Українська</a></li><li class="interlanguage-link interwiki-ur mw-list-item"><a href="https://ur.wikipedia.org/wiki/%D9%82%D8%AF%D8%B1%DB%8C_%D9%85%DB%8C%DA%A9%D8%A7%D9%86%DB%8C%D8%A7%D8%AA" title="قدری میکانیات – 乌尔都语" lang="ur" hreflang="ur" data-title="قدری میکانیات" data-language-autonym="اردو" data-language-local-name="乌尔都语" class="interlanguage-link-target">اردو</a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Kvant_mexanika" title="Kvant mexanika – 乌兹别克语" lang="uz" hreflang="uz" data-title="Kvant mexanika" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="乌兹别克语" class="interlanguage-link-target">Oʻzbekcha / ўзбекча</a></li><li class="interlanguage-link interwiki-vec mw-list-item"><a href="https://vec.wikipedia.org/wiki/Mec%C3%A0nega_cuant%C3%ACstega" title="Mecànega cuantìstega – 威尼斯语" lang="vec" hreflang="vec" data-title="Mecànega cuantìstega" data-language-autonym="Vèneto" data-language-local-name="威尼斯语" class="interlanguage-link-target">Vèneto</a></li><li class="interlanguage-link interwiki-vep mw-list-item"><a href="https://vep.wikipedia.org/wiki/Kvantmehanik" title="Kvantmehanik – 维普森语" lang="vep" hreflang="vep" data-title="Kvantmehanik" data-language-autonym="Vepsän kel’" data-language-local-name="维普森语" class="interlanguage-link-target">Vepsän kel’</a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/C%C6%A1_h%E1%BB%8Dc_l%C6%B0%E1%BB%A3ng_t%E1%BB%AD" title="Cơ học lượng tử – 越南语" lang="vi" hreflang="vi" data-title="Cơ học lượng tử" data-language-autonym="Tiếng Việt" data-language-local-name="越南语" class="interlanguage-link-target">Tiếng Việt</a></li><li class="interlanguage-link interwiki-war mw-list-item"><a href="https://war.wikipedia.org/wiki/Mekanika_kwantum" title="Mekanika kwantum – 瓦瑞语" lang="war" hreflang="war" data-title="Mekanika kwantum" data-language-autonym="Winaray" data-language-local-name="瓦瑞语" class="interlanguage-link-target">Winaray</a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6" title="量子力学 – 吴语" lang="wuu" hreflang="wuu" data-title="量子力学" data-language-autonym="吴语" data-language-local-name="吴语" class="interlanguage-link-target">吴语</a></li><li class="interlanguage-link interwiki-yi mw-list-item"><a href="https://yi.wikipedia.org/wiki/%D7%A7%D7%95%D7%95%D7%90%D7%A0%D7%98%D7%9F-%D7%9E%D7%A2%D7%9B%D7%90%D7%A0%D7%99%D7%A7" title="קוואנטן-מעכאניק – 意第绪语" lang="yi" hreflang="yi" data-title="קוואנטן-מעכאניק" data-language-autonym="ייִדיש" data-language-local-name="意第绪语" class="interlanguage-link-target">ייִדיש</a></li><li class="interlanguage-link interwiki-zh-classical mw-list-item"><a href="https://zh-classical.wikipedia.org/wiki/%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%B8" title="量子力學 – 文言文" lang="lzh" hreflang="lzh" data-title="量子力學" data-language-autonym="文言" data-language-local-name="文言文" class="interlanguage-link-target">文言</a></li><li class="interlanguage-link interwiki-zh-min-nan mw-list-item"><a href="https://zh-min-nan.wikipedia.org/wiki/Li%C5%8Dng-ch%C3%BA_le%CC%8Dk-ha%CC%8Dk" title="Liōng-chú le̍k-ha̍k – 闽南语" lang="nan" hreflang="nan" data-title="Liōng-chú le̍k-ha̍k" data-language-autonym="閩南語 / Bân-lâm-gú" data-language-local-name="闽南语" class="interlanguage-link-target">閩南語 / Bân-lâm-gú</a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%B8" title="量子力學 – 粤语" lang="yue" hreflang="yue" data-title="量子力學" data-language-autonym="粵語" data-language-local-name="粤语" class="interlanguage-link-target">粵語</a></li><li class="interlanguage-link interwiki-zu mw-list-item"><a href="https://zu.wikipedia.org/wiki/Ukuguxazela_kohoyana" title="Ukuguxazela kohoyana – 祖鲁语" lang="zu" hreflang="zu" data-title="Ukuguxazela kohoyana" data-language-autonym="IsiZulu" data-language-local-name="祖鲁语" class="interlanguage-link-target">IsiZulu</a></li> </ul> <div class="after-portlet after-portlet-lang"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q944#sitelinks-wikipedia" title="编辑跨语言链接" class="wbc-editpage">编辑链接</a></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div id="left-navigation"> <nav aria-label="命名空间"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-associated-pages" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-nstab-main" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6" title="浏览条目正文[c]" accesskey="c">条目</a></li><li id="ca-talk" class="vector-tab-noicon mw-list-item"><a href="/wiki/Talk:%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6" rel="discussion" title="关于此页面的讨论[t]" accesskey="t">讨论</a></li> </ul> </div> </div> <div id="vector-variants-dropdown" class="vector-dropdown " > <input type="checkbox" id="vector-variants-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-variants-dropdown" class="vector-dropdown-checkbox " aria-label="更改语言变体" > <label id="vector-variants-dropdown-label" for="vector-variants-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" >不转换 </label> <div class="vector-dropdown-content"> <div id="p-variants" class="vector-menu mw-portlet mw-portlet-variants" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-varlang-0" class="selected ca-variants-zh mw-list-item"><a href="/zh/%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6" lang="zh" hreflang="zh">不转换</a></li><li id="ca-varlang-1" class="ca-variants-zh-Hans mw-list-item"><a href="/zh-hans/%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6" lang="zh-Hans" hreflang="zh-Hans">简体</a></li><li id="ca-varlang-2" class="ca-variants-zh-Hant mw-list-item"><a href="/zh-hant/%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6" lang="zh-Hant" hreflang="zh-Hant">繁體</a></li><li id="ca-varlang-3" class="ca-variants-zh-Hans-CN mw-list-item"><a href="/zh-cn/%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6" lang="zh-Hans-CN" hreflang="zh-Hans-CN">大陆简体</a></li><li id="ca-varlang-4" class="ca-variants-zh-Hant-HK mw-list-item"><a href="/zh-hk/%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6" lang="zh-Hant-HK" hreflang="zh-Hant-HK">香港繁體</a></li><li id="ca-varlang-5" class="ca-variants-zh-Hant-MO mw-list-item"><a href="/zh-mo/%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6" lang="zh-Hant-MO" hreflang="zh-Hant-MO">澳門繁體</a></li><li id="ca-varlang-6" class="ca-variants-zh-Hans-MY mw-list-item"><a href="/zh-my/%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6" lang="zh-Hans-MY" hreflang="zh-Hans-MY">大马简体</a></li><li id="ca-varlang-7" class="ca-variants-zh-Hans-SG mw-list-item"><a href="/zh-sg/%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6" lang="zh-Hans-SG" hreflang="zh-Hans-SG">新加坡简体</a></li><li id="ca-varlang-8" class="ca-variants-zh-Hant-TW mw-list-item"><a href="/zh-tw/%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6" lang="zh-Hant-TW" hreflang="zh-Hant-TW">臺灣正體</a></li> </ul> </div> </div> </div> </div> </nav> </div> <div id="right-navigation" class="vector-collapsible"> <nav aria-label="查看"> <div id="p-views" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-views" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-view" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6">阅读</a></li><li id="ca-edit" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6&action=edit" title="编辑该页面[e]" accesskey="e">编辑</a></li><li id="ca-history" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6&action=history" title="本页面的早前版本。[h]" accesskey="h">查看历史</a></li> </ul> </div> </div> </nav> <nav class="vector-page-tools-landmark" aria-label="页面工具"> <div id="vector-page-tools-dropdown" class="vector-dropdown vector-page-tools-dropdown" > <input type="checkbox" id="vector-page-tools-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-tools-dropdown" class="vector-dropdown-checkbox " aria-label="工具" > <label id="vector-page-tools-dropdown-label" for="vector-page-tools-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" >工具 </label> <div class="vector-dropdown-content"> <div id="vector-page-tools-unpinned-container" class="vector-unpinned-container"> <div id="vector-page-tools" class="vector-page-tools vector-pinnable-element"> <div class="vector-pinnable-header vector-page-tools-pinnable-header vector-pinnable-header-unpinned" data-feature-name="page-tools-pinned" data-pinnable-element-id="vector-page-tools" data-pinned-container-id="vector-page-tools-pinned-container" data-unpinned-container-id="vector-page-tools-unpinned-container" > <div class="vector-pinnable-header-label">工具</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-page-tools.pin">移至侧栏</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-page-tools.unpin">隐藏</button> </div> <div id="p-cactions" class="vector-menu mw-portlet mw-portlet-cactions emptyPortlet vector-has-collapsible-items" title="更多选项" > <div class="vector-menu-heading"> 操作 </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-more-view" class="selected vector-more-collapsible-item mw-list-item"><a href="/wiki/%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6">阅读</a></li><li id="ca-more-edit" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6&action=edit" title="编辑该页面[e]" accesskey="e">编辑</a></li><li id="ca-more-history" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6&action=history">查看历史</a></li> </ul> </div> </div> <div id="p-tb" class="vector-menu mw-portlet mw-portlet-tb" > <div class="vector-menu-heading"> 常规 </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="t-whatlinkshere" class="mw-list-item"><a href="/wiki/Special:%E9%93%BE%E5%85%A5%E9%A1%B5%E9%9D%A2/%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6" title="列出所有与本页相链的页面[j]" accesskey="j">链入页面</a></li><li id="t-recentchangeslinked" class="mw-list-item"><a href="/wiki/Special:%E9%93%BE%E5%87%BA%E6%9B%B4%E6%94%B9/%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6" rel="nofollow" title="页面链出所有页面的更改[k]" accesskey="k">相关更改</a></li><li id="t-upload" class="mw-list-item"><a href="/wiki/Project:%E4%B8%8A%E4%BC%A0" title="上传图像或多媒体文件[u]" accesskey="u">上传文件</a></li><li id="t-specialpages" class="mw-list-item"><a href="/wiki/Special:%E7%89%B9%E6%AE%8A%E9%A1%B5%E9%9D%A2" title="全部特殊页面的列表[q]" accesskey="q">特殊页面</a></li><li id="t-permalink" class="mw-list-item"><a href="/w/index.php?title=%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6&oldid=84856400" title="此页面该修订版本的固定链接">固定链接</a></li><li id="t-info" class="mw-list-item"><a href="/w/index.php?title=%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6&action=info" title="关于此页面的更多信息">页面信息</a></li><li id="t-cite" class="mw-list-item"><a href="/w/index.php?title=Special:%E5%BC%95%E7%94%A8%E6%AD%A4%E9%A1%B5%E9%9D%A2&page=%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6&id=84856400&wpFormIdentifier=titleform" title="有关如何引用此页面的信息">引用此页</a></li><li id="t-urlshortener" class="mw-list-item"><a href="/w/index.php?title=Special:URL%E7%BC%A9%E7%9F%AD%E7%A8%8B%E5%BA%8F&url=https%3A%2F%2Fzh.wikipedia.org%2Fwiki%2F%25E9%2587%258F%25E5%25AD%2590%25E5%258A%259B%25E5%25AD%25A6">获取短链接</a></li><li id="t-urlshortener-qrcode" class="mw-list-item"><a href="/w/index.php?title=Special:QrCode&url=https%3A%2F%2Fzh.wikipedia.org%2Fwiki%2F%25E9%2587%258F%25E5%25AD%2590%25E5%258A%259B%25E5%25AD%25A6">下载二维码</a></li> </ul> </div> </div> <div id="p-electronpdfservice-sidebar-portlet-heading" class="vector-menu mw-portlet mw-portlet-electronpdfservice-sidebar-portlet-heading" > <div class="vector-menu-heading"> 打印/导出 </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="electron-print_pdf" class="mw-list-item"><a href="/w/index.php?title=Special:DownloadAsPdf&page=%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6&action=show-download-screen">下载为PDF</a></li><li id="t-print" class="mw-list-item"><a href="javascript:print();" rel="alternate" title="本页面的可打印版本[p]" accesskey="p">打印页面</a></li> </ul> </div> </div> <div id="p-wikibase-otherprojects" class="vector-menu mw-portlet mw-portlet-wikibase-otherprojects" > <div class="vector-menu-heading"> 在其他项目中 </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="wb-otherproject-link wb-otherproject-commons mw-list-item"><a href="https://commons.wikimedia.org/wiki/Category:Quantum_mechanics" hreflang="en">维基共享资源</a></li><li class="wb-otherproject-link wb-otherproject-wikibooks mw-list-item"><a href="https://zh.wikibooks.org/wiki/%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6" hreflang="zh">维基教科书</a></li><li class="wb-otherproject-link wb-otherproject-wikiquote mw-list-item"><a href="https://zh.wikiquote.org/wiki/%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%B8" hreflang="zh">维基语录</a></li><li id="t-wikibase" class="wb-otherproject-link wb-otherproject-wikibase-dataitem mw-list-item"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q944" title="链接到连接的数据仓库项目[g]" accesskey="g">维基数据项目</a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> </div> </div> </div> <div class="vector-column-end"> <div class="vector-sticky-pinned-container"> <nav class="vector-page-tools-landmark" aria-label="页面工具"> <div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="外观"> <div id="vector-appearance-pinned-container" class="vector-pinned-container"> <div id="vector-appearance" class="vector-appearance vector-pinnable-element"> <div class="vector-pinnable-header vector-appearance-pinnable-header vector-pinnable-header-pinned" data-feature-name="appearance-pinned" data-pinnable-element-id="vector-appearance" data-pinned-container-id="vector-appearance-pinned-container" data-unpinned-container-id="vector-appearance-unpinned-container" > <div class="vector-pinnable-header-label">外观</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">移至侧栏</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">隐藏</button> </div> </div> </div> </nav> </div> </div> <div id="bodyContent" class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> <div id="mw-indicator-GA" class="mw-indicator"><div class="mw-parser-output"><a href="/wiki/Wikipedia:%E4%BC%98%E8%89%AF%E6%9D%A1%E7%9B%AE" title="这是一篇优良条目，点击此处获取更多信息。"><img alt="这是一篇优良条目，点击此处获取更多信息。" src="//upload.wikimedia.org/wikipedia/commons/thumb/9/94/Symbol_support_vote.svg/24px-Symbol_support_vote.svg.png" decoding="async" width="24" height="25" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/94/Symbol_support_vote.svg/36px-Symbol_support_vote.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/94/Symbol_support_vote.svg/48px-Symbol_support_vote.svg.png 2x" data-file-width="180" data-file-height="185" /></a></div></div> <div id="mw-indicator-noteTA-b4dd506e" class="mw-indicator"><div class="mw-parser-output"><img alt="本页使用了标题或全文手工转换" src="//upload.wikimedia.org/wikipedia/commons/thumb/c/cd/Zh_conversion_icon_m.svg/35px-Zh_conversion_icon_m.svg.png" decoding="async" width="35" height="22" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/cd/Zh_conversion_icon_m.svg/53px-Zh_conversion_icon_m.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/cd/Zh_conversion_icon_m.svg/70px-Zh_conversion_icon_m.svg.png 2x" data-file-width="32" data-file-height="20" /></div></div> </div> <div id="siteSub" class="noprint">维基百科，自由的百科全书</div> </div> <div id="contentSub"><div id="mw-content-subtitle">（重定向自<a href="/w/index.php?title=%E9%87%8F%E5%AD%90%E7%89%A9%E7%90%86%E5%AD%B8&redirect=no" class="mw-redirect" title="量子物理學">量子物理學</a>）</div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="zh" dir="ltr"><div id="noteTA-b4dd506e" class="noteTA"><div class="noteTA-group"><div data-noteta-group-source="module" data-noteta-group="Physics"></div></div></div> <style data-mw-deduplicate="TemplateStyles:r85100532">.mw-parser-output .hatnote{font-size:small}.mw-parser-output div.hatnote{padding-left:2em;margin-bottom:0.8em;margin-top:0.8em}.mw-parser-output .hatnote-notice-img::after{content:"\202f \202f \202f \202f "}.mw-parser-output .hatnote-notice-img-small::after{content:"\202f \202f "}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}body.skin-minerva .mw-parser-output .hatnote-notice-img,body.skin-minerva .mw-parser-output .hatnote-notice-img-small{display:none}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable"><a href="/wiki/Wikipedia:%E6%B6%88%E6%AD%A7%E4%B9%89" title="Wikipedia:消歧义"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/5/5f/Disambig_gray.svg/25px-Disambig_gray.svg.png" decoding="async" width="25" height="19" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/5f/Disambig_gray.svg/38px-Disambig_gray.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/5f/Disambig_gray.svg/50px-Disambig_gray.svg.png 2x" data-file-width="220" data-file-height="168" /></a>关于本条目避免深奥术语、较容易理解的版本，请见「<a href="/wiki/%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%B8%E5%85%A5%E9%96%80" title="量子力學入門">量子力学入门</a>」。</div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Hydrogen_Density_Plots.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e7/Hydrogen_Density_Plots.png/290px-Hydrogen_Density_Plots.png" decoding="async" width="290" height="264" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e7/Hydrogen_Density_Plots.png/435px-Hydrogen_Density_Plots.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e7/Hydrogen_Density_Plots.png/580px-Hydrogen_Density_Plots.png 2x" data-file-width="2200" data-file-height="2000" /></a><figcaption>氫原子中<a href="/wiki/%E9%9B%BB%E5%AD%90" class="mw-redirect" title="電子">電子</a>在不同能階的<a href="/wiki/%E6%B3%A2%E5%87%BD%E6%95%B8" class="mw-redirect" title="波函數">波函數</a>。量子力學無法預測粒子在空間中的確切位置，只能預測在不同位置找到它的機率<a href="#cite_note-Born1926-1">[1]</a> 。較亮的區域代表找到電子的機率較高。</figcaption></figure> <style data-mw-deduplicate="TemplateStyles:r84265675">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline dl,.mw-parser-output .hlist.inline ol,.mw-parser-output .hlist.inline ul,.mw-parser-output .hlist dl dl,.mw-parser-output .hlist dl ol,.mw-parser-output .hlist dl ul,.mw-parser-output .hlist ol dl,.mw-parser-output .hlist ol ol,.mw-parser-output .hlist ol ul,.mw-parser-output .hlist ul dl,.mw-parser-output .hlist ul ol,.mw-parser-output .hlist ul ul{display:inline}.mw-parser-output .hlist .mw-empty-li{display:none}.mw-parser-output .hlist dt::after{content:" :"}.mw-parser-output .hlist dd::after,.mw-parser-output .hlist li::after{content:" · ";font-weight:bold}.mw-parser-output .hlist-pipe dd::after,.mw-parser-output .hlist-pipe li::after{content:" | ";font-weight:normal}.mw-parser-output .hlist-hyphen dd::after,.mw-parser-output .hlist-hyphen li::after{content:" - ";font-weight:normal}.mw-parser-output .hlist-comma dd::after,.mw-parser-output .hlist-comma li::after{content:"、";font-weight:normal}.mw-parser-output .hlist dd:last-child::after,.mw-parser-output .hlist dt:last-child::after,.mw-parser-output .hlist li:last-child::after{content:none}.mw-parser-output .hlist ol{counter-reset:listitem}.mw-parser-output .hlist ol>li{counter-increment:listitem}.mw-parser-output .hlist ol>li::before{content:" "counter(listitem)"\a0 "}.mw-parser-output .hlist dd ol>li:first-child::before,.mw-parser-output .hlist dt ol>li:first-child::before,.mw-parser-output .hlist li ol>li:first-child::before{content:"（"counter(listitem)"\a0 "}.mw-parser-output ul.cslist,.mw-parser-output ul.sslist{margin:0;padding:0;display:inline-block;list-style:none}.mw-parser-output .cslist li,.mw-parser-output .sslist li{margin:0;display:inline-block}.mw-parser-output .cslist li::after{content:"，"}.mw-parser-output .sslist li::after{content:"；"}.mw-parser-output .cslist li:last-child::after,.mw-parser-output .sslist li:last-child::after{content:none}</style><style data-mw-deduplicate="TemplateStyles:r82655520">.mw-parser-output .plainlist ol,.mw-parser-output .plainlist ul{line-height:inherit;list-style:none;margin:0;padding:0}.mw-parser-output .plainlist ol li,.mw-parser-output .plainlist ul li{margin-bottom:0}</style><style data-mw-deduplicate="TemplateStyles:r84913072">.mw-parser-output .sidebar{width:22em;float:right;clear:right;margin:0.5em 0 1em 1em;background:var(--background-color-neutral-subtle,#f8f9fa);border:1px solid var(--border-color-base,#a2a9b1);padding:0.2em;text-align:center;line-height:1.4em;font-size:88%;border-collapse:collapse;display:table}body.skin-minerva .mw-parser-output .sidebar{display:table!important;float:right!important;margin:0.5em 0 1em 1em!important}.mw-parser-output .sidebar-subgroup{width:100%;margin:0;border-spacing:0}.mw-parser-output .sidebar-left{float:left;clear:left;margin:0.5em 1em 1em 0}.mw-parser-output .sidebar-none{float:none;clear:both;margin:0.5em 1em 1em 0}.mw-parser-output .sidebar-outer-title{padding:0 0.4em 0.2em;font-size:125%;line-height:1.2em;font-weight:bold}.mw-parser-output .sidebar-top-image{padding:0.4em}.mw-parser-output .sidebar-top-caption,.mw-parser-output .sidebar-pretitle-with-top-image,.mw-parser-output .sidebar-caption{padding:0.2em 0.4em 0;line-height:1.2em}.mw-parser-output .sidebar-pretitle{padding:0.4em 0.4em 0;line-height:1.2em}.mw-parser-output .sidebar-title,.mw-parser-output .sidebar-title-with-pretitle{padding:0.2em 0.8em;font-size:145%;line-height:1.2em}.mw-parser-output .sidebar-title-with-pretitle{padding:0.1em 0.4em}.mw-parser-output .sidebar-image{padding:0.2em 0.4em 0.4em}.mw-parser-output .sidebar-heading{padding:0.1em 0.4em}.mw-parser-output .sidebar-content{padding:0 0.5em 0.4em}.mw-parser-output .sidebar-content-with-subgroup{padding:0.1em 0.4em 0.2em}.mw-parser-output .sidebar-above,.mw-parser-output .sidebar-below{padding:0.3em 0.8em;font-weight:bold}.mw-parser-output .sidebar-collapse .sidebar-above,.mw-parser-output .sidebar-collapse .sidebar-below{border-top:1px solid #aaa;border-bottom:1px solid #aaa}.mw-parser-output .sidebar-navbar{text-align:right;font-size:100%;padding:0 0.4em 0.4em}.mw-parser-output .sidebar-list-title{padding:0 0.4em;text-align:left;font-weight:bold;line-height:1.6em;font-size:105%}.mw-parser-output .sidebar-list-title-c{padding:0 0.4em;text-align:center;margin:0 3.3em}@media(max-width:640px){body.mediawiki .mw-parser-output .sidebar{width:100%!important;clear:both;float:none!important;margin-left:0!important;margin-right:0!important}}body.skin--responsive .mw-parser-output .sidebar a>img{max-width:none!important}@media screen{html.skin-theme-clientpref-night .mw-parser-output .sidebar:not(.notheme) .sidebar-list-title,html.skin-theme-clientpref-night .mw-parser-output .sidebar:not(.notheme) .sidebar-subgroup,html.skin-theme-clientpref-night .mw-parser-output .sidebar:not(.notheme) .sidebar-pretitle,html.skin-theme-clientpref-night .mw-parser-output .sidebar:not(.notheme) .sidebar-title,html.skin-theme-clientpref-night .mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle,html.skin-theme-clientpref-night .mw-parser-output .sidebar:not(.notheme) .sidebar-heading,html.skin-theme-clientpref-night .mw-parser-output .sidebar:not(.notheme) .sidebar-above,html.skin-theme-clientpref-night .mw-parser-output .sidebar:not(.notheme) .sidebar-below{background:inherit!important;color:inherit!important;border-color:#54595d!important}html.skin-theme-clientpref-night .mw-parser-output .sidebar a:not(.new):not(.mw-selflink):link{color:var(--color-progressive)!important}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .sidebar:not(.notheme) .sidebar-list-title,html.skin-theme-clientpref-os .mw-parser-output .sidebar:not(.notheme) .sidebar-subgroup,html.skin-theme-clientpref-os .mw-parser-output .sidebar:not(.notheme) .sidebar-pretitle,html.skin-theme-clientpref-os .mw-parser-output .sidebar:not(.notheme) .sidebar-title,html.skin-theme-clientpref-os .mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle,html.skin-theme-clientpref-os .mw-parser-output .sidebar:not(.notheme) .sidebar-heading,html.skin-theme-clientpref-os .mw-parser-output .sidebar:not(.notheme) .sidebar-above,html.skin-theme-clientpref-os .mw-parser-output .sidebar:not(.notheme) .sidebar-below{background:inherit!important;color:inherit!important;border-color:#54595d!important}html.skin-theme-clientpref-os .mw-parser-output .sidebar a:not(.new):not(.mw-selflink):link{color:var(--color-progressive)!important}}@media print{body.ns-0 .mw-parser-output .sidebar{display:none!important}}</style><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r84265675"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r84265675"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r84265675"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r84265675"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r84265675"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r84265675"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r84265675"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r84265675"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r84265675"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r84265675"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r84265675"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r84265675"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r84265675"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r84265675"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r84265675"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r84265675"><table class="sidebar sidebar-collapse nomobile nowraplinks plainlist nowraplinks" style="width:19.0em;"><tbody><tr><td class="sidebar-pretitle">系列条目</td></tr><tr><th class="sidebar-title-with-pretitle"><a class="mw-selflink selflink">量子力学</a></th></tr><tr><td class="sidebar-image"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle i\hbar {\frac {\partial }{\partial t}}|\psi (t)\rangle ={\hat {H}}|\psi (t)\rangle }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>i</mi> <mi class="MJX-variant">ℏ</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi mathvariant="normal">∂</mi> <mrow> <mi mathvariant="normal">∂</mi> <mi>t</mi> </mrow> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>ψ</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo fence="false" stretchy="false">⟩</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>H</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>ψ</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo fence="false" stretchy="false">⟩</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle i\hbar {\frac {\partial }{\partial t}}|\psi (t)\rangle ={\hat {H}}|\psi (t)\rangle }</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0de8741a7d26ae98689c7b3339e97dfafea9fd26" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:21.692ex; height:5.509ex;" alt="{\displaystyle i\hbar {\frac {\partial }{\partial t}}|\psi (t)\rangle ={\hat {H}}|\psi (t)\rangle }"><div class="sidebar-caption" style="font-size:90%;padding-top:0.4em;font-style:italic;"><a href="/wiki/%E8%96%9B%E5%AE%9A%E8%B0%94%E6%96%B9%E7%A8%8B" title="薛定谔方程">薛定谔方程</a></div></td></tr><tr><td class="sidebar-above hlist nowrap" style="display:block;margin-bottom:0.4em;"> <ul><li><a href="/wiki/%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%B8%E5%85%A5%E9%96%80" title="量子力學入門">入门</a></li> <li><a href="/w/index.php?title=%E5%88%9D%E7%BA%A7%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6%E8%AF%8D%E6%B1%87&action=edit&redlink=1" class="new" title="初级量子力学词汇（页面不存在）">术语</a>（英语：<a href="https://en.wikipedia.org/wiki/Glossary_of_elementary_quantum_mechanics" class="extiw" title="en:Glossary of elementary quantum mechanics">Glossary of elementary quantum mechanics</a>）</li> <li><a href="/wiki/%E7%89%A9%E7%90%86%E5%AD%A6%E5%8F%B2#量子理论" title="物理学史">历史</a></li></ul></td></tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="text-align:center;">背景</div><div class="sidebar-list-content mw-collapsible-content" style="border-top:1px solid #aaa;border-bottom:1px solid #aaa;"> <ul><li><a href="/wiki/%E7%BB%8F%E5%85%B8%E5%8A%9B%E5%AD%A6" title="经典力学">经典力学</a></li> <li><a href="/wiki/%E8%88%8A%E9%87%8F%E5%AD%90%E8%AB%96" title="舊量子論">舊量子論</a></li> <li><a href="/wiki/%E7%8B%84%E6%8B%89%E5%85%8B%E7%AC%A6%E5%8F%B7" title="狄拉克符号">狄拉克符号</a></li></ul> <div class="hlist" style="margin-left: 0em;"> <ul><li><a href="/wiki/%E5%93%88%E5%AF%86%E9%A1%BF%E7%AE%97%E7%AC%A6" title="哈密顿算符">哈密顿算符</a></li> <li><a href="/wiki/%E5%B9%B2%E6%B6%89_(%E7%89%A9%E7%90%86%E5%AD%A6)" title="干涉 (物理学)">干涉</a></li></ul> </div></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="text-align:center;">基本原理</div><div class="sidebar-list-content mw-collapsible-content" style="border-top:1px solid #aaa;border-bottom:1px solid #aaa;"><div class="hlist" style="margin-left: 0em;"> <ul><li><a href="/wiki/%E4%BA%92%E8%A1%A5%E5%8E%9F%E7%90%86" title="互补原理">互补</a></li> <li><a href="/wiki/%E9%87%8F%E5%AD%90%E9%80%80%E7%9B%B8%E5%B9%B2" title="量子退相干">退相干</a></li> <li><a href="/wiki/%E9%87%8F%E5%AD%90%E7%BA%8F%E7%B5%90" title="量子纏結">纠缠</a></li> <li><a href="/wiki/%E8%83%BD%E7%BA%A7" title="能级">能级</a></li> <li><a href="/wiki/%E9%87%8F%E5%AD%90%E6%B8%AC%E9%87%8F" title="量子測量">测量</a></li> <li><a href="/w/index.php?title=%E9%87%8F%E5%AD%90%E9%9D%9E%E5%B1%80%E5%9F%9F%E6%80%A7&action=edit&redlink=1" class="new" title="量子非局域性（页面不存在）">非局域性</a>（英语：<a href="https://en.wikipedia.org/wiki/Quantum_nonlocality" class="extiw" title="en:Quantum nonlocality">Quantum nonlocality</a>）</li> <li><a href="/wiki/%E9%87%8F%E5%AD%90%E6%95%B0" title="量子数">量子数</a></li> <li><a href="/wiki/%E9%87%8F%E5%AD%90%E6%85%8B" title="量子態">量子態</a></li> <li><a href="/wiki/%E6%80%81%E5%8F%A0%E5%8A%A0%E5%8E%9F%E7%90%86" title="态叠加原理">态叠加原理</a></li> <li><a href="/w/index.php?title=%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6%E4%B8%AD%E7%9A%84%E5%AF%B9%E7%A7%B0%E6%80%A7&action=edit&redlink=1" class="new" title="量子力学中的对称性（页面不存在）">对称性</a>（英语：<a href="https://en.wikipedia.org/wiki/Symmetry_in_quantum_mechanics" class="extiw" title="en:Symmetry in quantum mechanics">Symmetry in quantum mechanics</a>）</li> <li><a href="/wiki/%E9%87%8F%E5%AD%90%E7%A9%BF%E9%9A%A7%E6%95%88%E6%87%89" title="量子穿隧效應">量子穿隧效應</a></li> <li><a href="/wiki/%E4%B8%8D%E7%A1%AE%E5%AE%9A%E6%80%A7%E5%8E%9F%E7%90%86" title="不确定性原理">不确定性</a></li> <li><a href="/wiki/%E6%B3%A2%E5%87%BD%E6%95%B0" title="波函数">波函数</a> <ul><li><a href="/wiki/%E6%B3%A2%E5%87%BD%E6%95%B0%E5%9D%8D%E7%BC%A9" title="波函数坍缩">波函数坍缩</a></li></ul></li></ul> </div></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="text-align:center;">实验</div><div class="sidebar-list-content mw-collapsible-content" style="border-top:1px solid #aaa;border-bottom:1px solid #aaa;"><div class="hlist" style="margin-left: 0em;"> <ul><li><a href="/wiki/%E8%B2%9D%E7%88%BE%E5%AE%9A%E7%90%86%E7%9A%84%E5%AF%A6%E9%A9%97%E9%A9%97%E8%AD%89" title="貝爾定理的實驗驗證">貝爾定理的實驗驗證</a></li> <li><a href="/wiki/%E6%88%B4%E7%B6%AD%E6%A3%AE-%E9%9D%A9%E6%9C%AB%E5%AF%A6%E9%A9%97" title="戴維森-革末實驗">戴維森-革末實驗</a></li> <li><a href="/wiki/%E9%9B%99%E7%B8%AB%E5%AF%A6%E9%A9%97" title="雙縫實驗">雙縫實驗</a></li> <li><a href="/wiki/%E4%BC%8A%E5%88%A9%E6%BE%A4-%E5%A8%81%E5%BE%B7%E6%9B%BC%E7%82%B8%E5%BD%88%E6%B8%AC%E8%A9%A6%E5%95%8F%E9%A1%8C" title="伊利澤-威德曼炸彈測試問題">伊利澤-威德曼炸彈測試問題</a></li> <li><a href="/wiki/%E6%B3%95%E8%98%AD%E5%85%8B-%E8%B5%AB%E8%8C%B2%E5%AF%A6%E9%A9%97" title="法蘭克-赫茲實驗">法蘭克-赫茲實驗</a></li> <li><a href="/w/index.php?title=Leggett-Garg%E4%B8%8D%E5%B9%B3%E7%AD%89%E7%8E%B0%E8%B1%A1&action=edit&redlink=1" class="new" title="Leggett-Garg不平等现象（页面不存在）">Leggett-Garg不平等现象</a>（英语：<a href="https://en.wikipedia.org/wiki/Leggett%E2%80%93Garg_inequality" class="extiw" title="en:Leggett–Garg inequality">Leggett–Garg inequality</a>）</li> <li><a href="/wiki/%E9%A6%AC%E8%B5%AB-%E6%9B%BE%E5%BE%B7%E7%88%BE%E5%B9%B2%E6%B6%89%E5%84%80" title="馬赫-曾德爾干涉儀">馬赫-曾德爾干涉儀</a></li> <li><a href="/wiki/%E6%B3%A2%E6%99%AE%E5%B0%94%E5%AE%9E%E9%AA%8C" title="波普尔实验">波普尔实验</a></li></ul> </div> <ul><li><a href="/wiki/%E9%87%8F%E5%AD%90%E6%93%A6%E9%99%A4%E5%AF%A6%E9%A9%97" title="量子擦除實驗">量子擦除實驗</a> <ul><li><a href="/wiki/%E5%BB%B6%E9%81%B2%E9%81%B8%E6%93%87%E9%87%8F%E5%AD%90%E6%93%A6%E9%99%A4%E5%AF%A6%E9%A9%97" title="延遲選擇量子擦除實驗">延遲選擇</a></li></ul></li></ul> <div class="hlist" style="margin-left: 0em;"> <ul><li><a href="/wiki/%E8%96%9B%E5%AE%9A%E8%B0%94%E7%8C%AB" title="薛定谔猫">薛定谔猫</a></li> <li><a href="/wiki/%E6%96%BD%E7%89%B9%E6%81%A9-%E6%A0%BC%E6%8B%89%E8%B5%AB%E5%AE%9E%E9%AA%8C" title="施特恩-格拉赫实验">施特恩-格拉赫实验</a></li> <li><a href="/wiki/%E6%83%A0%E5%8B%92%E5%BB%B6%E8%BF%9F%E9%80%89%E6%8B%A9%E5%AE%9E%E9%AA%8C" title="惠勒延迟选择实验">惠勒延迟选择实验</a></li></ul> </div></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="text-align:center;">表述</div><div class="sidebar-list-content mw-collapsible-content" style="border-top:1px solid #aaa;border-bottom:1px solid #aaa;"> <ul><li><a href="/wiki/%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%B8%E7%9A%84%E6%95%B8%E5%AD%B8%E8%A1%A8%E8%BF%B0" title="量子力學的數學表述">概览</a></li></ul> <div class="hlist" style="margin-left: 0em;"> <ul><li><a href="/wiki/%E6%B5%B7%E6%A3%AE%E5%A0%A1%E7%B9%AA%E6%99%AF" title="海森堡繪景">海森堡繪景</a></li> <li><a href="/wiki/%E7%9B%B8%E4%BA%92%E4%BD%9C%E7%94%A8%E7%B9%AA%E6%99%AF" title="相互作用繪景">相互作用繪景</a></li> <li><a href="/wiki/%E7%9F%A9%E9%99%A3%E5%8A%9B%E5%AD%B8" title="矩陣力學">矩陣力學</a></li> <li><a href="/wiki/%E7%9B%B8%E7%A9%BA%E9%97%B4%E8%A1%A8%E8%BF%B0" title="相空间表述">相空间表述</a></li> <li><a href="/wiki/%E8%96%9B%E4%B8%81%E6%A0%BC%E7%B9%AA%E6%99%AF" title="薛丁格繪景">薛丁格繪景</a></li> <li><a href="/wiki/%E8%B7%AF%E5%BE%91%E7%A9%8D%E5%88%86%E8%A1%A8%E8%BF%B0" title="路徑積分表述">路徑積分表述</a></li></ul> </div></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="text-align:center;">方程</div><div class="sidebar-list-content mw-collapsible-content" style="border-top:1px solid #aaa;border-bottom:1px solid #aaa;"><div class="hlist" style="margin-left: 0em;"> <ul><li><a href="/wiki/%E7%8B%84%E6%8B%89%E5%85%8B%E6%96%B9%E7%A8%8B%E5%BC%8F" title="狄拉克方程式">狄拉克方程式</a></li> <li><a href="/wiki/%E5%85%8B%E8%8E%B1%E5%9B%A0-%E6%88%88%E5%B0%94%E7%99%BB%E6%96%B9%E7%A8%8B" title="克莱因-戈尔登方程">克莱因-戈尔登方程</a></li> <li><a href="/wiki/%E5%8C%85%E7%AB%8B%E6%96%B9%E7%A8%8B%E5%BC%8F" title="包立方程式">包立方程式</a></li> <li><a href="/wiki/%E9%87%8C%E5%BE%B7%E4%BC%AF%E5%85%AC%E5%BC%8F" title="里德伯公式">里德伯公式</a></li> <li><a href="/wiki/%E8%96%9B%E5%AE%9A%E8%B0%94%E6%96%B9%E7%A8%8B" title="薛定谔方程">薛定谔方程</a></li></ul> </div></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="text-align:center;">诠释</div><div class="sidebar-list-content mw-collapsible-content" style="border-top:1px solid #aaa;border-bottom:1px solid #aaa;"> <ul><li><a href="/wiki/%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%B8%E8%A9%AE%E9%87%8B" title="量子力學詮釋">概览</a></li></ul> <div class="hlist" style="margin-left: 0em;"> <ul><li><a href="/w/index.php?title=%E9%87%8F%E5%AD%90%E8%B4%9D%E5%8F%B6%E6%96%AF%E4%B8%BB%E4%B9%89&action=edit&redlink=1" class="new" title="量子贝叶斯主义（页面不存在）">量子贝叶斯主义</a>（英语：<a href="https://en.wikipedia.org/wiki/Quantum_Bayesianism" class="extiw" title="en:Quantum Bayesianism">Quantum Bayesianism</a>）</li> <li><a href="/wiki/%E4%B8%80%E8%87%B4%E6%80%A7%E5%8E%86%E5%8F%B2" title="一致性历史">一致性历史</a></li> <li><a href="/wiki/%E5%93%A5%E6%9C%AC%E5%93%88%E6%A0%B9%E8%A9%AE%E9%87%8B" title="哥本哈根詮釋">哥本哈根詮釋</a></li> <li><a href="/wiki/%E5%BE%B7%E5%B8%83%E7%BD%97%E6%84%8F-%E7%8E%BB%E5%A7%86%E7%90%86%E8%AE%BA" title="德布罗意-玻姆理论">德布罗意-玻姆理论</a></li> <li><a href="/wiki/%E7%B3%BB%E7%B6%9C%E8%A9%AE%E9%87%8B" title="系綜詮釋">系綜詮釋</a></li> <li><a href="/wiki/%E9%9A%B1%E8%AE%8A%E9%87%8F%E7%90%86%E8%AB%96" title="隱變量理論">隱變量理論</a> <ul><li><a href="/w/index.php?title=%E5%B1%80%E9%83%A8%E9%9A%90%E5%8F%98%E9%87%8F%E7%90%86%E8%AE%BA&action=edit&redlink=1" class="new" title="局部隐变量理论（页面不存在）">局部隐变量</a>（英语：<a href="https://en.wikipedia.org/wiki/Local_hidden-variable_theory" class="extiw" title="en:Local hidden-variable theory">Local hidden-variable theory</a>）</li></ul></li> <li><a href="/wiki/%E5%A4%9A%E4%B8%96%E7%95%8C%E8%AF%A0%E9%87%8A" title="多世界诠释">多世界诠释</a></li> <li><a href="/wiki/%E5%AE%A2%E8%A7%80%E5%9D%8D%E7%B8%AE%E7%90%86%E8%AB%96" title="客觀坍縮理論">客觀坍縮理論</a></li> <li><a href="/w/index.php?title=%E9%87%8F%E5%AD%90%E9%80%BB%E8%BE%91&action=edit&redlink=1" class="new" title="量子逻辑（页面不存在）">量子逻辑</a>（英语：<a href="https://en.wikipedia.org/wiki/Quantum_logic" class="extiw" title="en:Quantum logic">Quantum logic</a>）</li> <li><a href="/wiki/%E9%97%9C%E4%BF%82%E6%80%A7%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%B8" title="關係性量子力學">關係性量子力學</a></li> <li><a href="/wiki/%E4%BA%A4%E6%98%93%E8%A9%AE%E9%87%8B" title="交易詮釋">交易詮釋</a></li></ul> </div></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="text-align:center;">高阶</div><div class="sidebar-list-content mw-collapsible-content" style="border-top:1px solid #aaa;border-bottom:1px solid #aaa;"> <ul><li><a href="/wiki/%E7%9B%B8%E5%B0%8D%E8%AB%96%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%B8" class="mw-redirect" title="相對論量子力學">相对论量子力学</a>（英语：<a href="https://en.wikipedia.org/wiki/Relativistic_quantum_mechanics" class="extiw" title="en:Relativistic quantum mechanics">Relativistic quantum mechanics</a>）</li> <li><a href="/wiki/%E9%87%8F%E5%AD%90%E5%9C%BA%E8%AE%BA" title="量子场论">量子场论</a></li> <li><a href="/wiki/%E9%87%8F%E5%AD%90%E4%BF%A1%E6%81%AF%E7%A7%91%E5%AD%A6" title="量子信息科学">量子信息科学</a></li> <li><a href="/wiki/%E9%87%8F%E5%AD%90%E8%AE%A1%E7%AE%97%E6%9C%BA" title="量子计算机">量子计算</a></li> <li><a href="/w/index.php?title=%E9%87%8F%E5%AD%90%E6%B7%B7%E6%B2%8C&action=edit&redlink=1" class="new" title="量子混沌（页面不存在）">量子混沌</a>（英语：<a href="https://en.wikipedia.org/wiki/Quantum_chaos" class="extiw" title="en:Quantum chaos">Quantum chaos</a>）</li> <li><a href="/wiki/%E5%AF%86%E5%BA%A6%E7%9F%A9%E9%99%A3" title="密度矩陣">密度矩陣</a></li> <li><a href="/w/index.php?title=%E6%95%A3%E5%B0%84%E7%90%86%E8%AE%BA&action=edit&redlink=1" class="new" title="散射理论（页面不存在）">散射理论</a>（英语：<a href="https://en.wikipedia.org/wiki/Scattering_theory" class="extiw" title="en:Scattering theory">Scattering theory</a>）</li> <li><a href="/wiki/%E9%87%8F%E5%AD%90%E7%BB%9F%E8%AE%A1%E5%8A%9B%E5%AD%A6" title="量子统计力学">量子统计力学</a></li> <li><a href="/wiki/%E9%87%8F%E5%AD%90%E6%A9%9F%E5%99%A8%E5%AD%B8%E7%BF%92" title="量子機器學習">量子機器學習</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="text-align:center;">科学家</div><div class="sidebar-list-content mw-collapsible-content" style="border-top:1px solid #aaa;border-bottom:1px solid #aaa;"><div class="hlist" style="margin-left: 0em;"> <ul><li><a href="/wiki/%E4%BA%9A%E5%9F%BA%E5%B0%94%C2%B7%E9%98%BF%E5%93%88%E7%BD%97%E8%AF%BA%E5%A4%AB" title="亚基尔·阿哈罗诺夫">阿哈罗诺夫</a></li> <li><a href="/wiki/%E7%B4%84%E7%BF%B0%C2%B7%E8%B2%9D%E7%88%BE" class="mw-disambig" title="約翰·貝爾">貝爾</a></li> <li><a href="/wiki/%E6%B1%89%E6%96%AF%C2%B7%E8%B4%9D%E7%89%B9" title="汉斯·贝特">贝特</a></li> <li><a href="/wiki/%E5%B8%95%E7%89%B9%E9%87%8C%E5%85%8B%C2%B7%E5%B8%83%E8%8E%B1%E5%85%8B%E7%89%B9" title="帕特里克·布莱克特">布莱克特</a></li> <li><a href="/wiki/%E8%B4%B9%E5%88%A9%E5%85%8B%E6%96%AF%C2%B7%E5%B8%83%E6%B4%9B%E8%B5%AB" title="费利克斯·布洛赫">布洛赫</a></li> <li><a href="/wiki/%E6%88%B4%E7%BB%B4%C2%B7%E7%8E%BB%E5%A7%86" title="戴维·玻姆">玻姆</a></li> <li><a href="/wiki/%E5%B0%BC%E5%B0%94%E6%96%AF%C2%B7%E7%8E%BB%E5%B0%94" title="尼尔斯·玻尔">玻尔</a></li> <li><a href="/wiki/%E9%A9%AC%E5%85%8B%E6%96%AF%C2%B7%E7%8E%BB%E6%81%A9" title="马克斯·玻恩">玻恩</a></li> <li><a href="/wiki/%E8%96%A9%E7%89%B9%E5%BB%B6%E5%BE%B7%E6%8B%89%C2%B7%E7%B4%8D%E7%89%B9%C2%B7%E7%8E%BB%E8%89%B2" title="薩特延德拉·納特·玻色">玻色</a></li> <li><a href="/wiki/%E8%B7%AF%E6%98%93%C2%B7%E5%BE%B7%E5%B8%83%E7%BD%97%E6%84%8F" title="路易·德布罗意">德布罗意</a></li> <li><a href="/wiki/%E9%98%BF%E7%91%9F%C2%B7%E5%BA%B7%E6%99%AE%E9%A1%BF" title="阿瑟·康普顿">康普顿</a></li> <li><a href="/wiki/%E4%BF%9D%E7%BD%97%C2%B7%E7%8B%84%E6%8B%89%E5%85%8B" title="保罗·狄拉克">狄拉克</a></li> <li><a href="/wiki/%E5%85%8B%E6%9E%97%E9%A1%BF%C2%B7%E6%88%B4%E7%BB%B4%E5%AD%99" title="克林顿·戴维孙">戴维孙</a></li> <li><a href="/wiki/%E5%BD%BC%E5%BE%97%C2%B7%E5%BE%B7%E6%8B%9C" title="彼得·德拜">德拜</a></li> <li><a href="/wiki/%E4%BF%9D%E7%BD%97%C2%B7%E5%9F%83%E4%BC%A6%E8%B4%B9%E6%96%AF%E7%89%B9" title="保罗·埃伦费斯特">埃伦费斯特</a></li> <li><a href="/wiki/%E9%98%BF%E5%B0%94%E4%BC%AF%E7%89%B9%C2%B7%E7%88%B1%E5%9B%A0%E6%96%AF%E5%9D%A6" title="阿尔伯特·爱因斯坦">爱因斯坦</a></li> <li><a href="/wiki/%E4%BC%91%C2%B7%E8%89%BE%E5%BC%97%E9%9B%B7%E7%89%B9%E4%B8%89%E4%B8%96" title="休·艾弗雷特三世">艾弗雷特三世</a></li> <li><a href="/wiki/%E5%BC%97%E6%8B%89%E5%9F%BA%E7%B1%B3%E5%B0%94%C2%B7%E7%A6%8F%E5%85%8B" title="弗拉基米尔·福克">福克</a></li> <li><a href="/wiki/%E6%81%A9%E9%87%8C%E7%A7%91%C2%B7%E8%B4%B9%E7%B1%B3" title="恩里科·费米">费米</a></li> <li><a href="/wiki/%E7%90%86%E6%9F%A5%E5%BE%B7%C2%B7%E8%B2%BB%E6%9B%BC" title="理查德·費曼">費曼</a></li> <li><a href="/wiki/%E7%BD%97%E4%BC%8A%C2%B7%E6%A0%BC%E5%8A%B3%E4%BC%AF" title="罗伊·格劳伯">格劳伯</a></li> <li><a href="/wiki/%E5%8F%A4%E8%8C%A8%E5%A8%81%E5%8B%92" title="古茨威勒">古茨威勒</a></li> <li><a href="/wiki/%E7%BB%B4%E5%B0%94%E7%BA%B3%C2%B7%E6%B5%B7%E6%A3%AE%E5%A0%A1" title="维尔纳·海森堡">海森堡</a></li> <li><a href="/wiki/%E5%A4%A7%E5%8D%AB%C2%B7%E5%B8%8C%E5%B0%94%E4%BC%AF%E7%89%B9" title="大卫·希尔伯特">希尔伯特</a></li> <li><a href="/wiki/%E5%B8%95%E6%96%AF%E5%A4%B8%E5%B0%94%C2%B7%E7%BA%A6%E5%B0%94%E6%97%A6" class="mw-redirect" title="帕斯夸尔·约尔旦">约尔旦</a></li> <li><a href="/wiki/%E6%B1%89%E6%96%AF%C2%B7%E5%85%8B%E5%96%87%E6%9C%AB" title="汉斯·克喇末">克喇末</a></li> <li><a href="/wiki/%E6%B2%83%E5%B0%94%E5%A4%AB%E5%86%88%C2%B7%E6%B3%A1%E5%88%A9" title="沃尔夫冈·泡利">泡利</a></li> <li><a href="/wiki/%E5%A8%81%E5%88%A9%E6%96%AF%C2%B7%E5%85%B0%E5%A7%86" title="威利斯·兰姆">兰姆</a></li> <li><a href="/wiki/%E5%88%97%E5%A4%AB%C2%B7%E6%9C%97%E9%81%93" title="列夫·朗道">朗道</a></li> <li><a href="/wiki/%E9%A9%AC%E5%85%8B%E6%96%AF%C2%B7%E5%86%AF%C2%B7%E5%8A%B3%E5%8E%84" title="马克斯·冯·劳厄">劳厄</a></li> <li><a href="/wiki/%E4%BA%A8%E5%88%A9%C2%B7%E8%8E%AB%E5%A1%9E%E8%8E%B1" title="亨利·莫塞莱">莫塞莱</a></li> <li><a href="/wiki/%E7%BD%97%E4%BC%AF%E7%89%B9%C2%B7%E5%AF%86%E7%AB%8B%E6%A0%B9" title="罗伯特·密立根">密立根</a></li> <li><a href="/wiki/%E6%B5%B7%E5%85%8B%C2%B7%E5%8D%A1%E6%9C%AB%E6%9E%97%C2%B7%E6%98%82%E5%85%A7%E6%96%AF" title="海克·卡末林·昂內斯">昂內斯</a></li> <li><a href="/wiki/%E9%A9%AC%E5%85%8B%E6%96%AF%C2%B7%E6%99%AE%E6%9C%97%E5%85%8B" title="马克斯·普朗克">普朗克</a></li> <li><a href="/wiki/%E4%BC%8A%E8%A5%BF%E5%A4%9A%C2%B7%E6%8B%89%E6%AF%94" title="伊西多·拉比">拉比</a></li> <li><a href="/wiki/%E9%92%B1%E5%BE%B7%E6%8B%89%E5%A1%9E%E5%8D%A1%E6%8B%89%C2%B7%E6%8B%89%E6%9B%BC" title="钱德拉塞卡拉·拉曼">拉曼</a></li> <li><a href="/wiki/%E7%BA%A6%E7%BF%B0%E5%86%85%E6%96%AF%C2%B7%E9%87%8C%E5%BE%B7%E4%BC%AF" title="约翰内斯·里德伯">里德伯</a></li> <li><a href="/wiki/%E5%9F%83%E5%B0%94%E6%B8%A9%C2%B7%E8%96%9B%E5%AE%9A%E8%B0%94" title="埃尔温·薛定谔">薛定谔</a></li> <li><a href="/w/index.php?title=%E7%B1%B3%E6%AD%87%E5%B0%94%C2%B7%E8%A5%BF%E8%92%99%E6%96%AF&action=edit&redlink=1" class="new" title="米歇尔·西蒙斯（页面不存在）">米歇尔·西蒙斯</a>（英语：<a href="https://en.wikipedia.org/wiki/Michelle_Simmons" class="extiw" title="en:Michelle Simmons">Michelle Simmons</a>）</li> <li><a href="/wiki/%E9%98%BF%E8%AB%BE%C2%B7%E7%B4%A2%E6%9C%AB%E8%8F%B2" title="阿諾·索末菲">索末菲</a></li> <li><a href="/wiki/%E7%BA%A6%E7%BF%B0%C2%B7%E5%86%AF%C2%B7%E8%AF%BA%E4%BC%8A%E6%9B%BC" class="mw-redirect" title="约翰·冯·诺伊曼">冯·诺伊曼</a></li> <li><a href="/wiki/%E8%B5%AB%E5%B0%94%E6%9B%BC%C2%B7%E5%A4%96%E5%B0%94" title="赫尔曼·外尔">外尔</a></li> <li><a href="/wiki/%E5%A8%81%E5%BB%89%C2%B7%E7%BB%B4%E6%81%A9" title="威廉·维恩">维恩</a></li> <li><a href="/wiki/%E5%B0%A4%E9%87%91%C2%B7%E7%BB%B4%E6%A0%BC%E7%BA%B3" title="尤金·维格纳">维格纳</a></li> <li><a href="/wiki/%E5%BD%BC%E5%BE%97%C2%B7%E5%A1%9E%E6%9B%BC" title="彼得·塞曼">塞曼</a></li> <li><a href="/wiki/%E5%AE%89%E4%B8%9C%C2%B7%E8%94%A1%E6%9E%97%E6%A0%BC" title="安东·蔡林格">蔡林格</a></li></ul> </div></div></div></td> </tr><tr><td class="sidebar-navbar" style="line-height:1.6;border-top:1px solid #aaa;padding-top:0.1em;"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r84265675"><style data-mw-deduplicate="TemplateStyles:r84244141">.mw-parser-output .navbar{display:inline;font-weight:normal}.mw-parser-output .navbar-collapse{float:left;text-align:left}.mw-parser-output .navbar-boxtext{word-spacing:0}.mw-parser-output .navbar ul{display:inline-block;white-space:nowrap;line-height:inherit}.mw-parser-output .navbar-brackets::before{margin-right:-0.125em;content:"[ "}.mw-parser-output .navbar-brackets::after{margin-left:-0.125em;content:" ]"}.mw-parser-output .navbar li{word-spacing:-0.125em}.mw-parser-output .navbar a>span,.mw-parser-output .navbar a>abbr{text-decoration:inherit}.mw-parser-output .navbar-mini abbr{font-variant:small-caps;border-bottom:none;text-decoration:none;cursor:inherit}.mw-parser-output .navbar-ct-full{font-size:110%;margin:0 8em}.mw-parser-output .navbar-ct-mini{font-size:110%;margin:0 5em}html.skin-theme-clientpref-night .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}@media(prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}}@media print{.mw-parser-output .navbar{display:none!important}}</style><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%B8" title="Template:量子力學"><abbr title="查看该模板">查</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%B8" title="Template talk:量子力學"><abbr title="讨论该模板">论</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:%E7%BC%96%E8%BE%91%E9%A1%B5%E9%9D%A2/Template:%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%B8" title="Special:编辑页面/Template:量子力學"><abbr title="编辑该模板">编</abbr></a></li></ul></div></td></tr></tbody></table> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Solvay_conference_1927.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/6e/Solvay_conference_1927.jpg/250px-Solvay_conference_1927.jpg" decoding="async" width="250" height="181" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/6e/Solvay_conference_1927.jpg/375px-Solvay_conference_1927.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/6e/Solvay_conference_1927.jpg/500px-Solvay_conference_1927.jpg 2x" data-file-width="3000" data-file-height="2171" /></a><figcaption>1927年第五次<a href="/wiki/%E7%B4%A2%E5%B0%94%E7%BB%B4%E4%BC%9A%E8%AE%AE" title="索尔维会议">索尔维会议</a>，此次會議主題為「<a href="/wiki/%E9%9B%BB%E5%AD%90" class="mw-redirect" title="電子">電子</a>和<a href="/wiki/%E5%85%89%E5%AD%90" title="光子">光子</a>」，世界上最主要的物理學家聚集在一起討論新近表述的量子理論</figcaption></figure> 量子力学（quantum mechanics）是<a href="/wiki/%E7%89%A9%E7%90%86%E5%AD%B8" class="mw-redirect" title="物理學">物理學</a>的分支學科。它描述<a href="/wiki/%E5%8E%9F%E5%AD%90" title="原子">原子</a>尺度及原子尺度以下的<a href="/wiki/%E8%87%AA%E7%84%B6" title="自然">自然</a>行為<a href="#cite_note-Feynman-2">[2]</a>:1.1。它是所有量子物理學的基礎，包括<a href="/wiki/%E9%87%8F%E5%AD%90%E5%8C%96%E5%AD%B8" class="mw-redirect" title="量子化學">量子化學</a>、<a href="/wiki/%E9%87%8F%E5%AD%90%E5%A0%B4%E8%AB%96" class="mw-redirect" title="量子場論">量子場論</a>、<a href="/wiki/%E9%87%8F%E5%AD%90%E6%8A%80%E8%A1%93" title="量子技術">量子技術</a>、和<a href="/wiki/%E9%87%8F%E5%AD%90%E4%BF%A1%E6%81%AF%E7%A7%91%E5%AD%A6" title="量子信息科学">量子信息科学</a>。 量子力学与<a href="/wiki/%E7%9B%B8%E5%AF%B9%E8%AE%BA" title="相对论">相对论</a>一起被认为是<a href="/wiki/%E7%8F%BE%E4%BB%A3%E7%89%A9%E7%90%86%E5%AD%B8" title="現代物理學">现代物理学</a>的两大基本支柱。19世紀末，人們發現舊有的<a href="/wiki/%E5%8F%A4%E5%85%B8%E7%89%A9%E7%90%86%E5%AD%B8" class="mw-redirect" title="古典物理學">經典理論</a>無法解釋微观系统，於是經由<a href="/wiki/%E7%89%A9%E7%90%86%E5%AD%B8%E5%AE%B6" class="mw-redirect" title="物理學家">物理學家</a>的努力，在20世紀初創立量子力学，解釋了這些現象。量子力學從根本上改變人類對物質結構及其相互作用的理解。除了透过<a href="/wiki/%E5%B9%BF%E4%B9%89%E7%9B%B8%E5%AF%B9%E8%AE%BA" class="mw-redirect" title="广义相对论">广义相对论</a>描写的<a href="/wiki/%E4%B8%87%E6%9C%89%E5%BC%95%E5%8A%9B" class="mw-redirect" title="万有引力">引力</a>外，迄今所有<a href="/wiki/%E5%9F%BA%E6%9C%AC%E7%9B%B8%E4%BA%92%E4%BD%9C%E7%94%A8" title="基本相互作用">基本相互作用</a>均可以在量子力学的框架内描述（<a href="/wiki/%E9%87%8F%E5%AD%90%E5%9C%BA%E8%AE%BA" title="量子场论">量子场论</a>）。 量子理论的重要应用包括<a href="/wiki/%E5%AE%87%E5%AE%99%E5%AD%B8" class="mw-redirect" title="宇宙學">宇宙學</a>、<a href="/wiki/%E9%87%8F%E5%AD%90%E5%8C%96%E5%AD%A6" title="量子化学">量子化学</a>、<a href="/wiki/%E9%87%8F%E5%AD%90%E5%85%89%E5%AD%A6" title="量子光学">量子光学</a>、<a href="/wiki/%E9%87%8F%E5%AD%90%E8%AE%A1%E7%AE%97" class="mw-redirect" title="量子计算">量子计算</a>、<a href="/wiki/%E8%B6%85%E5%AF%BC%E7%A3%81%E4%BD%93" class="mw-redirect" title="超导磁体">超导磁体</a>、<a href="/wiki/%E5%8F%91%E5%85%89%E4%BA%8C%E6%9E%81%E7%AE%A1" class="mw-redirect" title="发光二极管">发光二极管</a>、<a href="/wiki/%E6%BF%80%E5%85%89%E5%99%A8" class="mw-redirect" title="激光器">激光器</a>、<a href="/wiki/%E6%99%B6%E4%BD%93%E7%AE%A1" title="晶体管">晶体管</a>和<a href="/wiki/%E5%8D%8A%E5%AF%BC%E4%BD%93" title="半导体">半导体</a>如<a href="/wiki/%E5%BE%AE%E5%A4%84%E7%90%86%E5%99%A8" title="微处理器">微处理器</a>等。 <a href="/wiki/%E6%84%9B%E5%9B%A0%E6%96%AF%E5%9D%A6" class="mw-redirect" title="愛因斯坦">愛因斯坦</a>可能是在科學文獻中最先給出術語「量子力學」的物理學者。<a href="#cite_note-Kragh2002-3">[3]</a>:86<a href="#cite_note-4">[a]</a> 量子力學<a href="/wiki/%E7%89%A9%E7%90%86%E5%AD%A6%E5%8F%B2#量子理论" title="物理学史">逐漸從理論中興起</a>，用來解釋與經典物理學不相符的觀測結果，例如<a href="/wiki/%E9%A6%AC%E5%85%8B%E6%96%AF%C2%B7%E6%99%AE%E6%9C%97%E5%85%8B" class="mw-redirect" title="馬克斯·普朗克">馬克斯·普朗克</a>在1900年解決<a href="/wiki/%E9%BB%91%E9%AB%94%E8%BC%BB%E5%B0%84" class="mw-redirect" title="黑體輻射">黑體輻射</a>問題，以及<a href="/wiki/%E9%98%BF%E7%88%BE%E4%BC%AF%E7%89%B9%C2%B7%E6%84%9B%E5%9B%A0%E6%96%AF%E5%9D%A6" class="mw-redirect" title="阿爾伯特·愛因斯坦">阿爾伯特·愛因斯坦</a><a href="/wiki/%E5%A5%87%E8%B9%9F%E5%B9%B4%E8%AB%96%E6%96%87" title="奇蹟年論文">1905年論文</a>中能量與頻率的對應關係，該論文解釋了<a href="/wiki/%E5%85%89%E7%94%B5%E6%95%88%E5%BA%94" title="光电效应">光电效应</a>影響。這些理解微觀現象的早期嘗試，現在被稱為“<a href="/wiki/%E8%88%8A%E9%87%8F%E5%AD%90%E8%AB%96" title="舊量子論">舊量子論</a>”，導致<a href="/wiki/%E5%B0%BC%E7%88%BE%E6%96%AF%C2%B7%E7%8E%BB%E7%88%BE" class="mw-redirect" title="尼爾斯·玻爾">尼爾斯·玻爾</a>、<a href="/wiki/%E6%AC%A7%E6%96%87%C2%B7%E8%96%9B%E5%AE%9A%E8%B0%94" class="mw-redirect" title="欧文·薛定谔">歐文·薛定諤</a>、<a href="/wiki/%E7%B6%AD%E7%88%BE%E7%B4%8D%C2%B7%E6%B5%B7%E6%A3%AE%E5%A0%A1" class="mw-redirect" title="維爾納·海森堡">維爾納·海森堡</a>、<a href="/wiki/%E9%A6%AC%E5%85%8B%E6%96%AF%C2%B7%E7%8E%BB%E6%81%A9" class="mw-redirect" title="馬克斯·玻恩">馬克斯·玻恩</a>、<a href="/wiki/%E4%BF%9D%E7%BD%97%C2%B7%E7%8B%84%E6%8B%89%E5%85%8B" title="保罗·狄拉克">保羅·狄拉克</a>等人在1920年代中期全面發展了量子力學。現代理論是用各種<a href="/wiki/%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%B8%E7%9A%84%E6%95%B8%E5%AD%B8%E8%A1%A8%E8%BF%B0" title="量子力學的數學表述">專門發展的數學形式體系來表達的</a>。其中之一，稱為<a href="/wiki/%E6%B3%A2%E5%87%BD%E6%95%B8" class="mw-redirect" title="波函數">波函數</a>的數學實體以<a href="/wiki/%E6%A9%9F%E7%8E%87%E5%B9%85" title="機率幅">機率幅</a>的形式提供有關粒子能量、動量和其他物理特性的測量結果的資訊。 <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="关键现象、歷史背景">关键现象、歷史背景</h2>[<a href="/w/index.php?title=%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6&action=edit&section=1" title="编辑章节：关键现象、歷史背景">编辑</a>]</div> <div class="mw-heading mw-heading3"><h3 id="黑体辐射">黑体辐射</h3>[<a href="/w/index.php?title=%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6&action=edit&section=2" title="编辑章节：黑体辐射">编辑</a>]</div> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:RWP-comparison.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/72/RWP-comparison.svg/200px-RWP-comparison.svg.png" decoding="async" width="200" height="160" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/72/RWP-comparison.svg/300px-RWP-comparison.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/72/RWP-comparison.svg/400px-RWP-comparison.svg.png 2x" data-file-width="600" data-file-height="480" /></a><figcaption><a href="/wiki/%E6%99%AE%E6%9C%97%E5%85%8B%E5%AE%9A%E5%BE%8B" class="mw-redirect" title="普朗克定律">普朗克定律</a>（绿）、<a href="/wiki/%E7%B6%AD%E6%81%A9%E5%AE%9A%E5%BE%8B" class="mw-redirect" title="維恩定律">維恩定律</a>（蓝）和<a href="/wiki/%E7%91%9E%E5%88%A9-%E9%87%91%E6%96%AF%E5%AE%9A%E5%BE%8B" title="瑞利-金斯定律">瑞利-金斯定律</a>（红）在频域下的比较，可见维恩定律在高频区域和普朗克定律相符，瑞利-金斯定律在低频区域和普朗克定律相符。</figcaption></figure> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r85100532"><div role="note" class="hatnote navigation-not-searchable">主条目：<a href="/wiki/%E9%BB%91%E4%BD%93%E8%BE%90%E5%B0%84" title="黑体辐射">黑体辐射</a></div> 理想<a href="/wiki/%E9%BB%91%E9%AB%94_(%E7%89%A9%E7%90%86%E5%AD%B8)" class="mw-redirect" title="黑體 (物理學)">黑体</a>可以吸收所有照射到它表面的<a href="/wiki/%E7%94%B5%E7%A3%81%E8%BE%90%E5%B0%84" class="mw-redirect" title="电磁辐射">電磁辐射</a>，并将这些辐射转化为<a href="/wiki/%E7%86%B1%E8%BC%BB%E5%B0%84" title="熱輻射">热辐射</a>，其光谱特征仅与该黑体的温度有关，與黑體的材質無關。从古典物理学出发推導出的<a href="/wiki/%E7%B6%AD%E6%81%A9%E5%AE%9A%E5%BE%8B" class="mw-redirect" title="維恩定律">維恩定律</a>在低頻區域與實驗數據不相符，而在高頻區域，从古典物理学的<a href="/wiki/%E8%83%BD%E9%87%8F%E5%9D%87%E5%88%86%E5%AE%9A%E7%90%86" title="能量均分定理">能量均分定理</a>推導出<a href="/wiki/%E7%91%9E%E5%88%A9-%E9%87%91%E6%96%AF%E5%AE%9A%E5%BE%8B" title="瑞利-金斯定律">瑞利-金斯定律</a>又與實驗數據不相符，在辐射频率趋向无穷大时，能量也會變得無窮大，這結果被称作“<a href="/wiki/%E7%B4%AB%E5%A4%96%E7%81%BE%E5%8F%98" title="紫外灾变">紫外灾变</a>”。然而在那時，普朗克並未注意到紫外灾变的嚴重性。 1900年12月14日，後來被定為量子力學的誕辰<a href="#cite_note-5">[4]</a>[<a href="/wiki/Wikipedia:%E5%8F%AF%E4%BE%9B%E6%9F%A5%E8%AD%89" title="Wikipedia:可供查證">查证请求</a>]，<a href="/wiki/%E9%A9%AC%E5%85%8B%E6%96%AF%C2%B7%E6%99%AE%E6%9C%97%E5%85%8B" title="马克斯·普朗克">马克斯·普朗克</a>在<a href="/wiki/%E6%9F%8F%E6%9E%97%E7%A7%91%E5%AD%B8%E9%99%A2" class="mw-redirect" title="柏林科學院">柏林科學院</a>發表報告，通過將維恩定律加以改良，又將<a href="/wiki/%E6%B3%A2%E8%8C%B2%E6%9B%BC%E7%86%B5%E5%85%AC%E5%BC%8F" title="波茲曼熵公式">波茲曼熵公式</a>重新詮釋，他得出了一个与实验数据完全吻合的<a href="/wiki/%E6%99%AE%E6%9C%97%E5%85%8B%E5%85%AC%E5%BC%8F" class="mw-redirect" title="普朗克公式">普朗克公式</a>来描述黑体辐射，但是在诠释这个公式时，他将在物体裡發射與吸收輻射的原子視為微小的<a href="/wiki/%E9%87%8F%E5%AD%90%E8%B0%90%E6%8C%AF%E5%AD%90" class="mw-redirect" title="量子谐振子">量子谐振子</a>，且假设这些量子谐振子的能量不是连续的，是离散的數值，而且單獨量子谐振子吸收和發射的辐射能是量子化的。<a href="#cite_note-Heisenberg1999-6">[5]</a>:第2章<a href="#cite_note-Kragh2002-3">[3]</a>:58-66<a href="#cite_note-Pais1982-7">[6]</a>:364-372 <div class="mw-heading mw-heading3"><h3 id="光电效应">光电效应</h3>[<a href="/w/index.php?title=%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6&action=edit&section=3" title="编辑章节：光电效应">编辑</a>]</div> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Photoelectric_effect_in_a_solid_-_diagram.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a6/Photoelectric_effect_in_a_solid_-_diagram.svg/200px-Photoelectric_effect_in_a_solid_-_diagram.svg.png" decoding="async" width="200" height="200" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a6/Photoelectric_effect_in_a_solid_-_diagram.svg/300px-Photoelectric_effect_in_a_solid_-_diagram.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a6/Photoelectric_effect_in_a_solid_-_diagram.svg/400px-Photoelectric_effect_in_a_solid_-_diagram.svg.png 2x" data-file-width="364" data-file-height="364" /></a><figcaption>光電效應示意圖：來自左上方的光子衝擊到金屬板，將電子逐出金屬板，且向右上方移去。</figcaption></figure> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r85100532"><div role="note" class="hatnote navigation-not-searchable">主条目：<a href="/wiki/%E5%85%89%E7%94%B5%E6%95%88%E5%BA%94" title="光电效应">光电效应</a></div> <a href="/wiki/%E6%B5%B7%E5%9B%A0%E9%87%8C%E5%B8%8C%C2%B7%E8%B5%AB%E5%85%B9" title="海因里希·赫兹">海因里希·赫兹</a>於1887年实验发现，如果照射<a href="/wiki/%E7%B4%AB%E5%A4%96%E5%85%89" class="mw-redirect" title="紫外光">紫外光</a>於金属表面，則电子會從金属表面被發射出来，他因此發現了<a href="/wiki/%E5%85%89%E9%9B%BB%E6%95%88%E6%87%89" class="mw-redirect" title="光電效應">光電效應</a>。1905年，<a href="/wiki/%E9%98%BF%E5%B0%94%E4%BC%AF%E7%89%B9%C2%B7%E7%88%B1%E5%9B%A0%E6%96%AF%E5%9D%A6" title="阿尔伯特·爱因斯坦">阿爾伯特·爱因斯坦</a>提出了光量子的理论来解释这个现象。他認為，光束是由一群離散的光量子所組成，而不是連續性波動。這些光量子現今被稱為<a href="/wiki/%E5%85%89%E5%AD%90" title="光子">光子</a>，其能量<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>E</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4232c9de2ee3eec0a9c0a19b15ab92daa6223f9b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.776ex; height:2.176ex;" alt="{\displaystyle E}">为 <dl><dd><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E=h\nu }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>E</mi> <mo>=</mo> <mi>h</mi> <mi>ν</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E=h\nu }</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c6c0386dc6d9530519404f95570fcc8548ed2326" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:7.445ex; height:2.176ex;" alt="{\displaystyle E=h\nu }"></dd></dl> 这裡，<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \nu }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ν</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \nu }</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c15bbbb971240cf328aba572178f091684585468" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.232ex; height:1.676ex;" alt="{\displaystyle \nu }"> 是<a href="/wiki/%E9%A0%BB%E7%8E%87_(%E7%89%A9%E7%90%86%E5%AD%B8)" title="頻率 (物理學)">頻率</a>，<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle h}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>h</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle h}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b26be3e694314bc90c3215047e4a2010c6ee184a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.339ex; height:2.176ex;" alt="{\displaystyle h}"> 為<a href="/wiki/%E6%99%AE%E6%9C%97%E5%85%8B%E5%B8%B8%E6%95%B8" class="mw-redirect" title="普朗克常數">普朗克常數</a>。 爱因斯坦大胆地预言，假若光子的频率高于金属的极限频率，则这光子可以给予足够能量来使得金属表面的一个电子逃逸，造成光电效应。电子获得的能量中，一部分被用来将金属中的电子射出，这部分能量叫<a href="/wiki/%E9%80%B8%E5%87%BA%E5%8A%9F" class="mw-redirect" title="逸出功">逸出功</a>，（用<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E_{\mbox{w}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>w</mtext> </mstyle> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E_{\mbox{w}}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d7c9dd3897eb3dcd9dcbae59712c6da0432c947f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.626ex; height:2.509ex;" alt="{\displaystyle E_{\mbox{w}}}">表示），另一部分成為了逃逸电子的動能： <dl><dd><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle h\nu =E_{\mbox{w}}+{\frac {1}{2}}mv^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>h</mi> <mi>ν</mi> <mo>=</mo> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>w</mtext> </mstyle> </mrow> </msub> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <mi>m</mi> <msup> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle h\nu =E_{\mbox{w}}+{\frac {1}{2}}mv^{2}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bbc6c4e721ab542e2700e3264968e985134ab022" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:18.356ex; height:5.176ex;" alt="{\displaystyle h\nu =E_{\mbox{w}}+{\frac {1}{2}}mv^{2}}"></dd></dl> 这裡 <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle m}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>m</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle m}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0a07d98bb302f3856cbabc47b2b9016692e3f7bc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.04ex; height:1.676ex;" alt="{\displaystyle m}"> 是电子的质量，<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle v}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>v</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle v}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e07b00e7fc0847fbd16391c778d65bc25c452597" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.128ex; height:1.676ex;" alt="{\displaystyle v}"> 是其速度。 假若光的频率低於金屬的極限頻率，那么它无法使得电子获得足够的逸出功。这时，不论<a href="/wiki/%E8%BC%BB%E7%85%A7%E5%BA%A6" title="輻照度">輻照度</a>有多大，照射時間有多長，都不會發生光電效應。而当入射光的頻率高於極限頻率時，即使光不夠強，當它射到金屬表面時也會觀察到光電子發射。<a href="/wiki/%E7%BE%85%E4%BC%AF%E7%89%B9%C2%B7%E5%AF%86%E7%AB%8B%E6%A0%B9" class="mw-redirect" title="羅伯特·密立根">羅伯特·密立根</a>後來的實驗證明這些理論與預言屬實。 爱因斯坦將普朗克的量子理论加以延伸擴展，他提出不仅仅物质与电磁辐射之间的相互作用是量子化的，而且量子化是一个基本物理特性的理论。通过这个新理论，他得以解释<a href="/wiki/%E5%85%89%E7%94%B5%E6%95%88%E5%BA%94" title="光电效应">光电效应</a>。<a href="#cite_note-Halliday-8">[7]</a>:1060-1063<a href="#cite_note-Kragh2002-3">[3]</a>:67-68 <div class="mw-heading mw-heading3"><h3 id="原子结构">原子结构</h3>[<a href="/w/index.php?title=%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6&action=edit&section=4" title="编辑章节：原子结构">编辑</a>]</div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r85100532"><div role="note" class="hatnote navigation-not-searchable">主条目：<a href="/wiki/%E5%8E%9F%E5%AD%90%E8%AB%96" title="原子論">原子論</a></div> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Bohr_atom_model.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/93/Bohr_atom_model.svg/200px-Bohr_atom_model.svg.png" decoding="async" width="200" height="174" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/93/Bohr_atom_model.svg/300px-Bohr_atom_model.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/93/Bohr_atom_model.svg/400px-Bohr_atom_model.svg.png 2x" data-file-width="310" data-file-height="270" /></a><figcaption>按照氫原子或類氫原子的玻爾模型，帶負價的電子被侷限於原子殼層，它們環繞著尺寸很小的帶正價原子核。電子從一個能量較高的軌道躍遷到能量較低的軌道時，會以電磁波的形式將能量差釋出。<a href="#cite_note-Akhlesh_Lakhtakia_Ed._1996-9">[8]</a>:49-82</figcaption></figure> 20世纪初，<a href="/wiki/%E5%8D%A2%E7%91%9F%E7%A6%8F%E6%A8%A1%E5%9E%8B" class="mw-redirect" title="卢瑟福模型">卢瑟福模型</a>被公认为正确的<a href="/wiki/%E5%8E%9F%E5%AD%90%E7%90%86%E8%AB%96" title="原子理論">原子模型</a>。这个模型假设带负电荷的电子，像行星围绕太阳运转一样，围绕带正电荷的<a href="/wiki/%E5%8E%9F%E5%AD%90%E6%A0%B8" title="原子核">原子核</a>运转。在这个过程中<a href="/wiki/%E5%BA%93%E4%BB%91%E5%AE%9A%E5%BE%8B" title="库仑定律">库仑力</a>与<a href="/wiki/%E7%A6%BB%E5%BF%83%E5%8A%9B" class="mw-redirect" title="离心力">离心力</a>必须平衡。 但是这个模型有两个问题无法解决。首先，按照經典电磁学，这个模型不稳定，由於电子不断地在它的运转过程中被加速，它应该會通过發射电磁波丧失能量，这样它很快就会坠入原子核。其次，实验结果显示，原子的<a href="/wiki/%E7%99%BC%E5%B0%84%E5%85%89%E8%AD%9C" title="發射光譜">发射光谱</a>是由一系列离散的发射线组成，比如<a href="/wiki/%E6%B0%A2%E5%8E%9F%E5%AD%90" class="mw-redirect" title="氢原子">氢原子</a>的发射光谱是由一个<a href="/wiki/%E7%B4%AB%E5%A4%96%E7%BA%BF" title="紫外线">紫外线</a>系列（<a href="/wiki/%E4%BE%86%E6%9B%BC%E7%B3%BB" title="來曼系">來曼系</a>）、一个可见光系列（<a href="/wiki/%E5%B7%B4%E8%80%B3%E9%BA%A5%E7%B3%BB" class="mw-redirect" title="巴耳麥系">巴耳麥系</a>）和其它的<a href="/wiki/%E7%BA%A2%E5%A4%96%E7%BA%BF" title="红外线">红外线</a>系列组成；而按照經典理论原子的发射谱应该是连续的。 1913年，<a href="/wiki/%E5%B0%BC%E5%B0%94%E6%96%AF%C2%B7%E7%8E%BB%E5%B0%94" title="尼尔斯·玻尔">尼尔斯·玻尔</a>提出了<a href="/wiki/%E7%8E%BB%E5%B0%94%E6%A8%A1%E5%9E%8B" title="玻尔模型">玻尔模型</a>，这个模型引入量子化的概念來解釋原子结构和光谱线。玻尔认为，电子只能在对应某些特定能量值<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E_{n}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E_{n}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ad6b82f2a00af6c9efd4c16d4e99329605645c0c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.934ex; height:2.509ex;" alt="{\displaystyle E_{n}}">的轨道上运動。假如一个电子，从一个能量比较高的轨道（<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E_{n}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E_{n}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ad6b82f2a00af6c9efd4c16d4e99329605645c0c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.934ex; height:2.509ex;" alt="{\displaystyle E_{n}}">），躍遷到一个能量比较低的轨道（<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E_{m}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E_{m}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3e2d5aa67bc4c46dfb5f6a1d674998ee81063a14" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.39ex; height:2.509ex;" alt="{\displaystyle E_{m}}">）上时，它发射的光的频率为 <dl><dd><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \nu ={\frac {E_{n}-E_{m}}{h}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ν</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> <mo>−</mo> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> </mrow> </msub> </mrow> <mi>h</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \nu ={\frac {E_{n}-E_{m}}{h}}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/45ec3f84f03bdff3d779087545723155124bccbb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:14.331ex; height:5.343ex;" alt="{\displaystyle \nu ={\frac {E_{n}-E_{m}}{h}}}"></dd></dl> 反之，通过吸收同样频率的光子，电子可以从低能的轨道，躍遷到高能的轨道上。 玻尔模型可以解释<a href="/wiki/%E6%B0%A2%E5%8E%9F%E5%AD%90" class="mw-redirect" title="氢原子">氢原子</a>的结构。改善的玻尔模型，还可以解释<a href="/wiki/%E9%A1%9E%E6%B0%AB%E5%8E%9F%E5%AD%90" title="類氫原子">類氫原子</a>的結構，即 He+, Li2+, Be3+ 等。但它还不够完善，仍然无法准确地解释其它原子的物理现象。<a href="#cite_note-Kragh2002-3">[3]</a>:53-57<a href="#cite_note-French1978-10">[9]</a>:24-29 <div class="mw-heading mw-heading3"><h3 id="物质波">物质波</h3>[<a href="/w/index.php?title=%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6&action=edit&section=5" title="编辑章节：物质波">编辑</a>]</div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r85100532"><div role="note" class="hatnote navigation-not-searchable">主条目：<a href="/wiki/%E7%89%A9%E8%B3%AA%E6%B3%A2" title="物質波">物質波</a></div> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Doubleslitexperiment_results_Tanamura_1.gif" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/79/Doubleslitexperiment_results_Tanamura_1.gif/200px-Doubleslitexperiment_results_Tanamura_1.gif" decoding="async" width="200" height="147" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/79/Doubleslitexperiment_results_Tanamura_1.gif/300px-Doubleslitexperiment_results_Tanamura_1.gif 1.5x, //upload.wikimedia.org/wikipedia/commons/7/79/Doubleslitexperiment_results_Tanamura_1.gif 2x" data-file-width="350" data-file-height="257" /></a><figcaption><a href="/w/index.php?title=%E5%A4%96%E6%9D%91%E5%BD%B0&action=edit&redlink=1" class="new" title="外村彰（页面不存在）">外村彰</a>（日语：<a href="https://ja.wikipedia.org/wiki/%E5%A4%96%E6%9D%91%E5%BD%B0" class="extiw" title="ja:外村彰">外村彰</a>）（Akira Tonomura）團隊做電子雙縫實驗得到的干涉圖樣：每秒約有1000個電子抵達探測屏，電子與電子之間的距離約為150km，兩個電子同時存在於電子發射器與探測屏之間的概率微乎其微。圖中每一亮點表示一個電子抵達探測屏，<a href="#cite_note-ElectronDetection-12">[b]</a>經過一段時間，電子的累積顯示出干涉圖樣。<a href="#cite_note-Tonomura1988-13">[11]</a></figcaption></figure> 1924年，<a href="/wiki/%E8%B7%AF%E6%98%93%C2%B7%E5%BE%B7%E5%B8%83%E7%BD%97%E6%84%8F" title="路易·德布罗意">路易·德布罗意</a>發表博士論文提出，粒子拥有波动性，其波长<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \lambda _{Broglie}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> <mi>r</mi> <mi>o</mi> <mi>g</mi> <mi>l</mi> <mi>i</mi> <mi>e</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \lambda _{Broglie}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8787677df4d10e6cbbcb5ccb70daa3beed0ecb5c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:6.987ex; height:2.843ex;" alt="{\displaystyle \lambda _{Broglie}}">与动量<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle p}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>p</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/81eac1e205430d1f40810df36a0edffdc367af36" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.089ex; width:1.259ex; height:2.009ex;" alt="{\displaystyle p}">成反比，以方程式表示為<a href="#cite_note-14">[12]</a> <dl><dd><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \lambda _{Broglie}={\frac {h}{p}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> <mi>r</mi> <mi>o</mi> <mi>g</mi> <mi>l</mi> <mi>i</mi> <mi>e</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>h</mi> <mi>p</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \lambda _{Broglie}={\frac {h}{p}}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/de02675e124925973f0f639bc890d7ea75e6a2cb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:12.26ex; height:5.843ex;" alt="{\displaystyle \lambda _{Broglie}={\frac {h}{p}}}">。</dd></dl> 這理論稱為<a href="/wiki/%E5%BE%B7%E5%B8%83%E7%BE%85%E6%84%8F%E5%81%87%E8%AA%AA" class="mw-redirect" title="德布羅意假說">德布羅意假說</a>，又稱為<a href="/wiki/%E5%BE%B7%E5%B8%83%E7%BE%85%E6%84%8F%E5%81%87%E8%AA%AA" class="mw-redirect" title="德布羅意假說">物質波假說</a>。這意味著電子不但具有粒子性，還具有波動性。 1927年，<a href="/wiki/%E5%85%8B%E6%9E%97%E9%A1%BF%C2%B7%E6%88%B4%E7%BB%B4%E6%A3%AE" class="mw-redirect" title="克林顿·戴维森">克林顿·戴维森</a>與<a href="/wiki/%E9%9B%B7%E6%96%AF%E7%89%B9%C2%B7%E9%9D%A9%E6%9C%AB" title="雷斯特·革末">雷斯特·革末</a>做實驗將低能量電子入射於鎳晶體，然後測量對於每一個角度的散射強度。從分析實驗數據，他們發現，假設加速電勢為5.4eV，則在50°之處會出現強勁反射，符合<a href="/wiki/%E5%A8%81%E5%BB%89%C2%B7%E5%B8%83%E6%8B%89%E6%A0%BC" class="mw-redirect" title="威廉·布拉格">威廉·布拉格</a>於1913年所提出的 <a href="/wiki/X%E5%B0%84%E7%B7%9A" class="mw-redirect" title="X射線">X射線</a>繞射性質。這驚人的結果證實電子是一種物質波，也證實了物質波假說。這實驗就是著名的<a href="/wiki/%E6%88%B4%E7%B6%AD%E6%A3%AE%EF%BC%8D%E9%9D%A9%E6%9C%AB%E5%AF%A6%E9%A9%97" class="mw-redirect" title="戴維森－革末實驗">戴維森－革末實驗</a>。<a href="#cite_note-French1978-10">[9]</a>:64-68 电子的<a href="/wiki/%E5%8F%8C%E7%BC%9D%E5%AE%9E%E9%AA%8C" class="mw-redirect" title="双缝实验">双缝实验</a>可以非常生动地展示出多种不同的量子力学现象。<a href="#cite_note-Feynman_2006-15">[13]</a>如右图所示， <ul><li>打在屏幕上的电子是点状的，这个现象与一般感受到的点状的粒子相同。<a href="#cite_note-ElectronDetection-12">[b]</a></li> <li>电子打在屏幕上的位置，有一定的分布概率，随时间可以看出双缝衍射所特有的条纹图像。假如一个光缝被关闭的话，所形成的图像是单缝特有的波的分布概率。</li></ul> 在图中的实验裡，电子源的强度非常低，所發射出的電子與電子之間的距離約為150km，任意兩個電子同時存在於電子發射器與探測屏之間的概率微乎其微。显然可以推斷，單獨电子同时通过了两條狹缝，自己與自己發生干涉，从而出現这个干涉圖樣。对于經典物理学来说，这个解释非常奇怪。从量子力学的角度来看，电子的分布概率可以用两个分別通过两條狹縫的<a href="/wiki/%E9%87%8F%E5%AD%90%E6%85%8B" title="量子態">量子态</a>疊加在一起來解釋。这个实验非常具有信服力地展示出電子的波動性。<a href="#cite_note-Tonomura1988-13">[11]</a> <div class="mw-heading mw-heading2"><h2 id="数学基础">数学基础</h2>[<a href="/w/index.php?title=%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6&action=edit&section=6" title="编辑章节：数学基础">编辑</a>]</div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r85100532"><div role="note" class="hatnote navigation-not-searchable">主条目：<a href="/wiki/%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6%E7%9A%84%E6%95%B0%E5%AD%A6%E8%A1%A8%E8%BF%B0" class="mw-redirect" title="量子力学的数学表述">量子力学的数学表述</a></div> 在二十世紀二十年代，出现了两种量子物理的理论，即<a href="/wiki/%E7%BB%B4%E5%B0%94%E7%BA%B3%C2%B7%E6%B5%B7%E6%A3%AE%E5%A0%A1" title="维尔纳·海森堡">维尔纳·海森堡</a>的<a href="/wiki/%E7%9F%A9%E9%98%B5%E5%8A%9B%E5%AD%A6" class="mw-redirect" title="矩阵力学">矩阵力学</a>和<a href="/wiki/%E5%9F%83%E5%B0%94%E6%B8%A9%C2%B7%E8%96%9B%E5%AE%9A%E8%B0%94" title="埃尔温·薛定谔">埃尔温·薛定谔</a>的<a href="/wiki/%E6%B3%A2%E5%8B%95%E5%8A%9B%E5%AD%B8" title="波動力學">波动力学</a>。 海森堡主張，只有在實驗裏能夠觀察到的物理量（<a href="/wiki/%E5%8F%AF%E8%A7%80%E5%AF%9F%E9%87%8F" title="可觀察量">可觀察量</a>），才具有物理意義，才可以用理論描述其物理行為，例如，不能直接觀察到電子運動於原子裏的位置與週期。因此，他著重於研究電子躍遷時所發射光波的離散頻率和<a href="/wiki/%E8%BC%BB%E7%85%A7%E5%BA%A6" title="輻照度">輻照度</a>，這些是可觀察量。但是，他無法實際應用這點子於<a href="/wiki/%E6%B0%AB%E5%8E%9F%E5%AD%90" title="氫原子">氫原子</a>問題，因為這問題太過複雜，他只能改應用這點子於比較簡單，但也比較不實際的問題。經過一番努力，他計算出<a href="/wiki/%E8%AB%A7%E6%8C%AF%E5%AD%90" title="諧振子">諧振子</a>問題的<a href="/wiki/%E7%99%BC%E5%B0%84%E5%85%89%E8%AD%9C" title="發射光譜">能譜</a>與<a href="/wiki/%E9%9B%B6%E9%BB%9E%E8%83%BD%E9%87%8F" title="零點能量">零點能量</a>，符合<a href="/wiki/%E5%85%89%E8%AD%9C%E5%AD%B8" class="mw-redirect" title="光譜學">分子光譜學</a>的結果。另外，在海森堡理論中，系統的<a href="/wiki/%E5%93%88%E5%AF%86%E9%A0%93%E9%87%8F" class="mw-redirect" title="哈密頓量">哈密頓量</a>是位置和動量的函數，但它們不再具有古典力學中的定義，而是由二階（代表著過程的初態和終態）<a href="/wiki/%E5%82%85%E7%AB%8B%E5%8F%B6%E5%8F%98%E6%8D%A2" class="mw-redirect" title="傅立叶变换">傅立葉係數</a>的矩陣給出。海森堡還發現，這些矩陣互不<a href="/wiki/%E5%B0%8D%E6%98%93%E9%97%9C%E4%BF%82" class="mw-redirect" title="對易關係">對易</a>。這些論述後來發展成為矩陣力學。<a href="#cite_note-Kragh2002-3">[3]</a>:161-163 從<a href="/wiki/%E5%BE%B7%E5%B8%83%E7%BD%97%E6%84%8F" class="mw-redirect" title="德布罗意">德布羅意</a>論文的相對論性理論，薛定谔推導出一種波動方程式，稱為<a href="/wiki/%E8%96%9B%E4%B8%81%E6%A0%BC%E6%96%B9%E7%A8%8B%E5%BC%8F" class="mw-redirect" title="薛丁格方程式">薛定谔方程式</a>；用這方程式可以計算出氫原子的譜線，得到與<a href="/wiki/%E6%B3%A2%E8%80%B3%E6%A8%A1%E5%9E%8B" class="mw-redirect" title="波耳模型">波耳模型</a>完全相同的答案。波动力学的基礎方程式就是薛定谔方程式<a href="#cite_note-Kragh2002-3">[3]</a>:163-164 薛定谔率先於1926年证明了这两种理论的等价性。稍后，<a href="/w/index.php?title=%E5%8D%A1%E7%88%BE%C2%B7%E5%9F%83%E5%8D%A1%E7%89%B9&action=edit&redlink=1" class="new" title="卡爾·埃卡特（页面不存在）">卡爾·埃卡特</a>（英语：<a href="https://en.wikipedia.org/wiki/Carl_Eckart" class="extiw" title="en:Carl Eckart">Carl Eckart</a>）和<a href="/wiki/%E6%B2%83%E7%88%BE%E5%A4%AB%E5%B2%A1%C2%B7%E5%8C%85%E7%AB%8B" class="mw-redirect" title="沃爾夫岡·包立">沃爾夫岡·包立</a>也给出類似证明，<a href="#cite_note-Kragh2002-3">[3]</a>:166<a href="/wiki/%E7%BA%A6%E7%BF%B0%C2%B7%E5%86%AF%C2%B7%E8%AF%BA%E4%BC%8A%E6%9B%BC" class="mw-redirect" title="约翰·冯·诺伊曼">约翰·冯·诺伊曼</a>严格地证明了波动力学和矩阵力学的等价性。<a href="#cite_note-Neumann1932-16">[14]</a> <div class="mw-heading mw-heading3"><h3 id="基礎公設">基礎公設</h3>[<a href="/w/index.php?title=%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6&action=edit&section=7" title="编辑章节：基礎公設">编辑</a>]</div> 整個量子力学的数学理论可以建立於五个基礎公設(postulate)。這些公設不能被嚴格推導出來，而是從實驗結果仔細分析归纳总结而得到的。從這五個公設，可以推導出整個量子力學。假若量子力學的理論結果不符合實驗結果，則必須將這些基礎公設加以修改，直到沒有任何不符合之處。至今為止，量子力學已被實驗核對至極高準確度，還沒有找到任何與理論不符合的實驗結果，雖然有些理論很難直覺地用經典物理的概念來理解，例如，<a href="/wiki/%E6%B3%A2%E7%B2%92%E4%BA%8C%E8%B1%A1%E6%80%A7" title="波粒二象性">波粒二象性</a>、<a href="/wiki/%E9%87%8F%E5%AD%90%E7%BA%A0%E7%BC%A0" class="mw-redirect" title="量子纠缠">量子糾纏</a>等等。<a href="#cite_note-17">[15]</a><a href="#cite_note-Laloë-18">[16]</a>:211ff<a href="#cite_note-Zettili2009-19">[17]</a>:165-167 <ol><li>量子態公設：量子系统在任意时刻的状态（量子態）可以由<a href="/wiki/%E5%B8%8C%E5%B0%94%E4%BC%AF%E7%89%B9%E7%A9%BA%E9%97%B4" title="希尔伯特空间">希尔伯特空间</a> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathcal {H}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">H</mi> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {H}}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/19ef4c7b923a5125ac91aa491838a95ee15b804f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.964ex; height:2.176ex;" alt="{\displaystyle {\mathcal {H}}}"> 中的態矢量 <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle |\psi \rangle }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>ψ</mi> <mo fence="false" stretchy="false">⟩</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle |\psi \rangle }</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cc27f1893b769a08cd6b296e115a29e61cab675e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:3.065ex; height:2.843ex;" alt="{\displaystyle |\psi \rangle }"> 来設定，這態矢量完備地給出了這量子系統的所有信息。這公設意味著量子系統遵守<a href="/wiki/%E6%80%81%E5%8F%A0%E5%8A%A0%E5%8E%9F%E7%90%86" title="态叠加原理">态叠加原理</a>，假若<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle |\psi _{1}\rangle }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <msub> <mi>ψ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo fence="false" stretchy="false">⟩</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle |\psi _{1}\rangle }</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7917a2e2cb0d3c7191f41a4f7ee250f4d4c56fd2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.119ex; height:2.843ex;" alt="{\displaystyle |\psi _{1}\rangle }">、<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle |\psi _{2}\rangle }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <msub> <mi>ψ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo fence="false" stretchy="false">⟩</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle |\psi _{2}\rangle }</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d9cace1b140a568a4b9a90587dde3b342266bcf1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.119ex; height:2.843ex;" alt="{\displaystyle |\psi _{2}\rangle }">屬於希尔伯特空间<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathcal {H}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">H</mi> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {H}}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/19ef4c7b923a5125ac91aa491838a95ee15b804f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.964ex; height:2.176ex;" alt="{\displaystyle {\mathcal {H}}}">，則<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle c_{1}|\psi _{1}\rangle +c_{2}|\psi _{2}\rangle }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <msub> <mi>ψ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo fence="false" stretchy="false">⟩</mo> <mo>+</mo> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <msub> <mi>ψ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo fence="false" stretchy="false">⟩</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle c_{1}|\psi _{1}\rangle +c_{2}|\psi _{2}\rangle }</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2e9e6fd63171bf5bc72469a842ebfe4b29d1b499" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:15.2ex; height:2.843ex;" alt="{\displaystyle c_{1}|\psi _{1}\rangle +c_{2}|\psi _{2}\rangle }">也屬於希尔伯特空间<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathcal {H}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">H</mi> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {H}}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/19ef4c7b923a5125ac91aa491838a95ee15b804f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.964ex; height:2.176ex;" alt="{\displaystyle {\mathcal {H}}}">，其中<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle c_{1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle c_{1}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/77b7dc6d279091d354e0b90889b463bfa7eb7247" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.061ex; height:2.009ex;" alt="{\displaystyle c_{1}}">和<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle c_{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle c_{2}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0b30ba1b247fb8d334580cec68561e749d24aff2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.061ex; height:2.009ex;" alt="{\displaystyle c_{2}}">皆為常數。</li> <li>時間演化公設：态矢量為 <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle |\psi (t)\rangle }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>ψ</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo fence="false" stretchy="false">⟩</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle |\psi (t)\rangle }</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fe09d6c91bfdbae7a3aaa7f0ae7ff6b96f521eca" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:5.714ex; height:2.843ex;" alt="{\displaystyle |\psi (t)\rangle }"> 的量子系統，其动力学演化可以用<a href="/wiki/%E8%96%9B%E5%AE%9A%E8%B0%94%E6%96%B9%E7%A8%8B#含時薛定諤方程" title="薛定谔方程">薛定谔方程</a>表示，<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle i\hbar {\frac {\partial }{\partial t}}|\psi (t)\rangle ={\hat {H}}|\psi (t)\rangle }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>i</mi> <mi class="MJX-variant">ℏ</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi mathvariant="normal">∂</mi> <mrow> <mi mathvariant="normal">∂</mi> <mi>t</mi> </mrow> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>ψ</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo fence="false" stretchy="false">⟩</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>H</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>ψ</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo fence="false" stretchy="false">⟩</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle i\hbar {\frac {\partial }{\partial t}}|\psi (t)\rangle ={\hat {H}}|\psi (t)\rangle }</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0de8741a7d26ae98689c7b3339e97dfafea9fd26" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:21.692ex; height:5.509ex;" alt="{\displaystyle i\hbar {\frac {\partial }{\partial t}}|\psi (t)\rangle ={\hat {H}}|\psi (t)\rangle }"> ；其中，<a href="/wiki/%E5%93%88%E5%AF%86%E9%A1%BF%E7%AE%97%E7%AC%A6" title="哈密顿算符">哈密顿算符</a> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\hat {H}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>H</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\hat {H}}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6bb06de5217295d7fbdbf68fb9c5309a513fc99e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.064ex; height:2.843ex;" alt="{\displaystyle {\hat {H}}}"> 对应於量子系统的总能量，<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \hbar }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi class="MJX-variant">ℏ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \hbar }</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/de68de3a92517953436c93b5a76461d49160cc41" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.306ex; height:2.176ex;" alt="{\displaystyle \hbar }">是<a href="/wiki/%E7%BA%A6%E5%8C%96%E6%99%AE%E6%9C%97%E5%85%8B%E5%B8%B8%E6%95%B0" class="mw-redirect" title="约化普朗克常数">約化普朗克常數</a>。根據薛定谔方程，假設時間從<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle t_{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle t_{0}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/02d3006c4190b1939b04d9b9bb21006fb4e6fa4a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.894ex; height:2.343ex;" alt="{\displaystyle t_{0}}">流动到<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle t}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>t</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle t}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/65658b7b223af9e1acc877d848888ecdb4466560" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.84ex; height:2.009ex;" alt="{\displaystyle t}">，則態向量從<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle |\psi (t_{0})\rangle }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>ψ</mi> <mo stretchy="false">(</mo> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo stretchy="false">)</mo> <mo fence="false" stretchy="false">⟩</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle |\psi (t_{0})\rangle }</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/812f09b74e43997eb26ea7de291ad182c32efad2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.768ex; height:2.843ex;" alt="{\displaystyle |\psi (t_{0})\rangle }">演化到 <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle |\psi (t)\rangle }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>ψ</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo fence="false" stretchy="false">⟩</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle |\psi (t)\rangle }</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fe09d6c91bfdbae7a3aaa7f0ae7ff6b96f521eca" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:5.714ex; height:2.843ex;" alt="{\displaystyle |\psi (t)\rangle }"> ，這過程以方程式表示為<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle |\psi (t)\rangle ={\hat {U}}(t,t_{0})|\psi (t_{0})\rangle }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>ψ</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo fence="false" stretchy="false">⟩</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>U</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mo stretchy="false">(</mo> <mi>t</mi> <mo>,</mo> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>ψ</mi> <mo stretchy="false">(</mo> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo stretchy="false">)</mo> <mo fence="false" stretchy="false">⟩</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle |\psi (t)\rangle ={\hat {U}}(t,t_{0})|\psi (t_{0})\rangle }</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/92618cd788099a7b1be86c0d324f161dee9a8dda" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:22.939ex; height:3.343ex;" alt="{\displaystyle |\psi (t)\rangle ={\hat {U}}(t,t_{0})|\psi (t_{0})\rangle }"> ；其中，<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\hat {U}}(t,t_{0})=e^{-i{\hat {H}}(t-t_{0})/\hbar }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>U</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mo stretchy="false">(</mo> <mi>t</mi> <mo>,</mo> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo stretchy="false">)</mo> <mo>=</mo> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mi>i</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>H</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mo stretchy="false">(</mo> <mi>t</mi> <mo>−</mo> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi class="MJX-variant">ℏ</mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\hat {U}}(t,t_{0})=e^{-i{\hat {H}}(t-t_{0})/\hbar }}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f9ef0e2cf3758291130dcc893ff7538ef4ec1379" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:21.401ex; height:3.676ex;" alt="{\displaystyle {\hat {U}}(t,t_{0})=e^{-i{\hat {H}}(t-t_{0})/\hbar }}"> 是時間演化算符。</li> <li>可觀察量公設：每個<a href="/wiki/%E5%8F%AF%E8%A7%82%E5%AF%9F%E9%87%8F" class="mw-redirect" title="可观察量">可观察量</a> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7daff47fa58cdfd29dc333def748ff5fa4c923e3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle A}"> 都有其對應的<a href="/wiki/%E5%8E%84%E7%B1%B3%E7%AE%97%E7%AC%A6" class="mw-redirect" title="厄米算符">厄米算符</a> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\hat {A}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>A</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\hat {A}}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f595a6c73d1183d6a1b2ac21fe47ac28c1483821" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.776ex; height:2.843ex;" alt="{\displaystyle {\hat {A}}}"> ，而算符<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\hat {A}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>A</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\hat {A}}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f595a6c73d1183d6a1b2ac21fe47ac28c1483821" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.776ex; height:2.843ex;" alt="{\displaystyle {\hat {A}}}">的所有本徵矢量共同組成一個完備<a href="/wiki/%E5%9F%BA%E5%BA%95" class="mw-redirect" title="基底">基底</a>。</li> <li>塌縮公設：對於量子系統測量某個可觀察量 <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7daff47fa58cdfd29dc333def748ff5fa4c923e3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle A}"> ，這動作可以數學表示為將其對應的厄米算符<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\hat {A}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>A</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\hat {A}}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f595a6c73d1183d6a1b2ac21fe47ac28c1483821" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.776ex; height:2.843ex;" alt="{\displaystyle {\hat {A}}}"> 作用於量子系統的態矢量 <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle |\psi \rangle }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>ψ</mi> <mo fence="false" stretchy="false">⟩</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle |\psi \rangle }</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cc27f1893b769a08cd6b296e115a29e61cab675e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:3.065ex; height:2.843ex;" alt="{\displaystyle |\psi \rangle }"> ，測量值只能為厄米算符<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\hat {A}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>A</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\hat {A}}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f595a6c73d1183d6a1b2ac21fe47ac28c1483821" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.776ex; height:2.843ex;" alt="{\displaystyle {\hat {A}}}"> 的本徵值。在測量後，假設測量值為<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a_{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a_{i}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0bc77764b2e74e64a63341054fa90f3e07db275f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.029ex; height:2.009ex;" alt="{\displaystyle a_{i}}">，則量子系統的量子態立刻會塌縮為對應於本徵值<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a_{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a_{i}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0bc77764b2e74e64a63341054fa90f3e07db275f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.029ex; height:2.009ex;" alt="{\displaystyle a_{i}}">的本徵態 <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle |e_{i}\rangle }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <msub> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo fence="false" stretchy="false">⟩</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle |e_{i}\rangle }</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a63d3b7d08f454cc1799a34aedb965f56416ae97" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:3.435ex; height:2.843ex;" alt="{\displaystyle |e_{i}\rangle }"> 。</li> <li><a href="/wiki/%E7%8E%BB%E6%81%A9%E5%AE%9A%E5%89%87" title="玻恩定則">波恩公設</a>：對於這測量，獲得本徵值 <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a_{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a_{i}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0bc77764b2e74e64a63341054fa90f3e07db275f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.029ex; height:2.009ex;" alt="{\displaystyle a_{i}}"> 的概率為量子態<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle |\psi \rangle }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>ψ</mi> <mo fence="false" stretchy="false">⟩</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle |\psi \rangle }</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cc27f1893b769a08cd6b296e115a29e61cab675e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:3.065ex; height:2.843ex;" alt="{\displaystyle |\psi \rangle }">處於本徵態<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle |e_{i}\rangle }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <msub> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo fence="false" stretchy="false">⟩</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle |e_{i}\rangle }</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a63d3b7d08f454cc1799a34aedb965f56416ae97" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:3.435ex; height:2.843ex;" alt="{\displaystyle |e_{i}\rangle }">的<a href="/w/index.php?title=%E6%A6%82%E7%8E%87%E5%B9%85&action=edit&redlink=1" class="new" title="概率幅（页面不存在）">概率幅</a>的絕對值平方。<a href="#cite_note-20">[c]</a></li></ol> <div class="mw-heading mw-heading3"><h3 id="量子態與量子算符">量子態與量子算符</h3>[<a href="/w/index.php?title=%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6&action=edit&section=8" title="编辑章节：量子態與量子算符">编辑</a>]</div> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Stern-Gerlach_experiment_zh.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/b4/Stern-Gerlach_experiment_zh.png/250px-Stern-Gerlach_experiment_zh.png" decoding="async" width="250" height="156" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b4/Stern-Gerlach_experiment_zh.png/375px-Stern-Gerlach_experiment_zh.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/b4/Stern-Gerlach_experiment_zh.png/500px-Stern-Gerlach_experiment_zh.png 2x" data-file-width="520" data-file-height="324" /></a><figcaption>設定<a href="/wiki/%E6%96%AF%E7%89%B9%E6%81%A9-%E9%9D%A9%E6%8B%89%E8%B5%AB%E5%AF%A6%E9%A9%97" class="mw-redirect" title="斯特恩-革拉赫實驗">斯特恩-革拉赫實驗</a>儀器的磁場方向為z-軸，入射的銀原子束可以被分裂成兩道銀原子束，每一道銀原子束代表一種量子態，上旋<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left\vert \uparrow \right\rangle }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>|</mo> <mo stretchy="false">↑</mo> <mo>⟩</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left\vert \uparrow \right\rangle }</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/40e620003115eac7fb280bc1dcc220a3b1598c43" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:2.714ex; height:2.843ex;" alt="{\displaystyle \left\vert \uparrow \right\rangle }">或下旋<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left\vert \downarrow \right\rangle }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>|</mo> <mo stretchy="false">↓</mo> <mo>⟩</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left\vert \downarrow \right\rangle }</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1c8f6c3d8dddbe5bd4b229cd911f11c2f5e6daed" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:2.714ex; height:2.843ex;" alt="{\displaystyle \left\vert \downarrow \right\rangle }">。<a href="#cite_note-Sakurai-21">[18]</a>:1-4</figcaption></figure> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r85100532"><div role="note" class="hatnote navigation-not-searchable">主条目：<a href="/wiki/%E9%87%8F%E5%AD%90%E6%85%8B" title="量子態">量子態</a>和<a href="/wiki/%E7%AE%97%E7%AC%A6" title="算符">算符</a></div> <a href="/wiki/%E9%87%8F%E5%AD%90%E6%85%8B" title="量子態">量子態</a>指的是量子系統的狀態，<a href="/wiki/%E6%85%8B%E5%90%91%E9%87%8F" title="態向量">態向量</a>可以用來抽象地表現量子態。採用<a href="/wiki/%E7%8B%84%E6%8B%89%E5%85%8B%E6%A8%99%E8%A8%98" class="mw-redirect" title="狄拉克標記">狄拉克標記</a>，態向量表示為<a href="/wiki/%E7%8B%84%E6%8B%89%E5%85%8B%E6%A8%99%E8%A8%98" class="mw-redirect" title="狄拉克標記">右矢</a><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left\vert \psi \right\rangle }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>|</mo> <mi>ψ</mi> <mo>⟩</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left\vert \psi \right\rangle }</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6e6a3a7d6221a16c2eff2d7ec038c3f8313a8240" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:3.065ex; height:2.843ex;" alt="{\displaystyle \left\vert \psi \right\rangle }">；其中，在符號內部的希臘字母<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \psi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ψ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \psi }</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/45e5789e5d9c8f7c79744f43ecaaf8ba42a8553a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.513ex; height:2.509ex;" alt="{\displaystyle \psi }">可以是任何符號，字母，數字，或單字。例如，沿著<a href="/wiki/%E7%A3%81%E5%A0%B4" title="磁場">磁場</a>方向測量<a href="/wiki/%E9%9B%BB%E5%AD%90" class="mw-redirect" title="電子">電子</a>的<a href="/wiki/%E8%87%AA%E6%97%8B" title="自旋">自旋</a>，得到的結果可以是上旋或是下旋，分別標記為<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left\vert \uparrow \right\rangle }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>|</mo> <mo stretchy="false">↑</mo> <mo>⟩</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left\vert \uparrow \right\rangle }</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/40e620003115eac7fb280bc1dcc220a3b1598c43" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:2.714ex; height:2.843ex;" alt="{\displaystyle \left\vert \uparrow \right\rangle }">或<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left\vert \downarrow \right\rangle }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>|</mo> <mo stretchy="false">↓</mo> <mo>⟩</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left\vert \downarrow \right\rangle }</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1c8f6c3d8dddbe5bd4b229cd911f11c2f5e6daed" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:2.714ex; height:2.843ex;" alt="{\displaystyle \left\vert \downarrow \right\rangle }">。<a href="#cite_note-Griffiths2004-22">[19]</a>:93-96 對量子態做<a href="/wiki/%E6%93%8D%E4%BD%9C%E5%AE%9A%E4%B9%89" title="操作定义">操作定義</a>，量子態可以從一系列製備程序來辨認，即這程序所製成的量子系統擁有這量子態。<a href="#cite_note-Laloe-23">[20]</a>:15-16例如，使用<a href="/wiki/%E6%96%AF%E7%89%B9%E6%81%A9-%E9%9D%A9%E6%8B%89%E8%B5%AB%E5%AF%A6%E9%A9%97" class="mw-redirect" title="斯特恩-革拉赫實驗">斯特恩-革拉赫實驗</a>儀器，設定磁場朝著z-軸方向，如右圖所示，可以將入射的銀原子束，依照自旋的z-分量分裂成兩道，一道為上旋，量子態為<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left\vert \uparrow \right\rangle }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>|</mo> <mo stretchy="false">↑</mo> <mo>⟩</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left\vert \uparrow \right\rangle }</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/40e620003115eac7fb280bc1dcc220a3b1598c43" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:2.714ex; height:2.843ex;" alt="{\displaystyle \left\vert \uparrow \right\rangle }">，另一道為下旋，量子態為<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left\vert \downarrow \right\rangle }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>|</mo> <mo stretchy="false">↓</mo> <mo>⟩</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left\vert \downarrow \right\rangle }</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1c8f6c3d8dddbe5bd4b229cd911f11c2f5e6daed" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:2.714ex; height:2.843ex;" alt="{\displaystyle \left\vert \downarrow \right\rangle }">，這樣，可以製備成量子態為<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left\vert \uparrow \right\rangle }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>|</mo> <mo stretchy="false">↑</mo> <mo>⟩</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left\vert \uparrow \right\rangle }</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/40e620003115eac7fb280bc1dcc220a3b1598c43" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:2.714ex; height:2.843ex;" alt="{\displaystyle \left\vert \uparrow \right\rangle }">的銀原子束，或量子態為<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left\vert \downarrow \right\rangle }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>|</mo> <mo stretchy="false">↓</mo> <mo>⟩</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left\vert \downarrow \right\rangle }</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1c8f6c3d8dddbe5bd4b229cd911f11c2f5e6daed" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:2.714ex; height:2.843ex;" alt="{\displaystyle \left\vert \downarrow \right\rangle }">的銀原子束。原本銀原子束的態向量可以按照<a href="/wiki/%E6%80%81%E5%8F%A0%E5%8A%A0%E5%8E%9F%E7%90%86" title="态叠加原理">態疊加原理</a>表示為<a href="#cite_note-Sakurai-21">[18]</a>:1-4 <dl><dd><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left\vert \psi \right\rangle =\alpha \left\vert \uparrow \right\rangle +\beta \left\vert \downarrow \right\rangle }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>|</mo> <mi>ψ</mi> <mo>⟩</mo> </mrow> <mo>=</mo> <mi>α</mi> <mrow> <mo>|</mo> <mo stretchy="false">↑</mo> <mo>⟩</mo> </mrow> <mo>+</mo> <mi>β</mi> <mrow> <mo>|</mo> <mo stretchy="false">↓</mo> <mo>⟩</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left\vert \psi \right\rangle =\alpha \left\vert \uparrow \right\rangle +\beta \left\vert \downarrow \right\rangle }</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d7bfac9b4220542cb3c794a35d8f4149e7520607" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:18.025ex; height:2.843ex;" alt="{\displaystyle \left\vert \psi \right\rangle =\alpha \left\vert \uparrow \right\rangle +\beta \left\vert \downarrow \right\rangle }">；</dd></dl> 其中，<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \alpha }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>α</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \alpha }</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b79333175c8b3f0840bfb4ec41b8072c83ea88d3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.488ex; height:1.676ex;" alt="{\displaystyle \alpha }">、<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \beta }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>β</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \beta }</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7ed48a5e36207156fb792fa79d29925d2f7901e8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.332ex; height:2.509ex;" alt="{\displaystyle \beta }">是複值係數，<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle |\alpha |^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>α</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle |\alpha |^{2}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fa34618537661f2d4d710cc26e8afe891f50f7b8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:3.836ex; height:3.343ex;" alt="{\displaystyle |\alpha |^{2}}">、<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle |\beta |^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>β</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle |\beta |^{2}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4caecb560883af3b9c0c3a1d0e13aae75f121d0d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:3.68ex; height:3.343ex;" alt="{\displaystyle |\beta |^{2}}">分別為入射銀原子束處於上旋、下旋的概率，<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle |\alpha |^{2}+|\beta |^{2}=1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>α</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>β</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle |\alpha |^{2}+|\beta |^{2}=1}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/18cd7473cdb894839d10852890517b1fb687c73b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:14.617ex; height:3.343ex;" alt="{\displaystyle |\alpha |^{2}+|\beta |^{2}=1}">。 在斯特恩-革拉赫實驗裏，可以透過測量而得到自旋的z-分量，這種物理量稱為<a href="/wiki/%E5%8F%AF%E8%A7%80%E5%AF%9F%E9%87%8F" title="可觀察量">可觀察量</a>，透過做實驗測量可以得到其測值。每一個可觀察量都有一個對應的<a href="/wiki/%E7%AE%97%E7%AC%A6" title="算符">量子算符</a>；將算符作用於量子態，會使得量子態線性變換成另一個量子態。假若變換前的量子態與變換後的量子態，除了乘法數值以外，兩個量子態相同，則稱此量子態為此算符的<a href="/wiki/%E6%9C%AC%E5%BE%B5%E6%85%8B" class="mw-redirect" title="本徵態">本徵態</a>，稱此乘法數值為此算符的<a href="/wiki/%E6%9C%AC%E5%BE%81%E5%80%BC" class="mw-redirect" title="本征值">本徵值</a>。<a href="#cite_note-Sakurai-21">[18]</a>:11-12可觀察量的算符也許會有很多本徵值與本徵態。根據<a href="/wiki/%E7%B5%B1%E8%A8%88%E8%A9%AE%E9%87%8B" class="mw-redirect" title="統計詮釋">統計詮釋</a>，每一次測量所得到的測值只能是其中的一個本徵值，而且，測得這本徵值的機會呈概率性，量子系統的量子態也會改變為對應於本徵值的本徵態。<a href="#cite_note-Griffiths2004-22">[19]</a>:106-109例如，自旋的z-分量是個<a href="/wiki/%E5%8F%AF%E8%A7%80%E5%AF%9F%E9%87%8F" title="可觀察量">可觀察量</a><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle S_{z}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>z</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S_{z}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bf685f2b7d1c4266b32c1e16fdc6a41a610ab21e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.427ex; height:2.509ex;" alt="{\displaystyle S_{z}}">，做實驗可以得到的測值為<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle +\hbar /2}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>+</mo> <mi class="MJX-variant">ℏ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle +\hbar /2}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/354b144f3a401ae92414a417e63197ef2b7b4a4b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:5.44ex; height:2.843ex;" alt="{\displaystyle +\hbar /2}">或<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle -\hbar /2}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>−</mo> <mi class="MJX-variant">ℏ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle -\hbar /2}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9e0bc5875fe0b0a5b3cb2fd489159c2c2156bfc1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:5.44ex; height:2.843ex;" alt="{\displaystyle -\hbar /2}">。對應於<a href="/wiki/%E5%8F%AF%E8%A7%80%E5%AF%9F%E9%87%8F" title="可觀察量">可觀察量</a><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle S_{z}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>z</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S_{z}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bf685f2b7d1c4266b32c1e16fdc6a41a610ab21e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.427ex; height:2.509ex;" alt="{\displaystyle S_{z}}">的量子算符<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\hat {S}}_{z}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>S</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>z</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\hat {S}}_{z}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7ac67cb8315ba14707385264d2f64e1e65a965f2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.574ex; height:3.176ex;" alt="{\displaystyle {\hat {S}}_{z}}">有兩個本徵值分別為<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle +\hbar /2}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>+</mo> <mi class="MJX-variant">ℏ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle +\hbar /2}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/354b144f3a401ae92414a417e63197ef2b7b4a4b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:5.44ex; height:2.843ex;" alt="{\displaystyle +\hbar /2}">、<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle -\hbar /2}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>−</mo> <mi class="MJX-variant">ℏ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle -\hbar /2}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9e0bc5875fe0b0a5b3cb2fd489159c2c2156bfc1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:5.44ex; height:2.843ex;" alt="{\displaystyle -\hbar /2}">的本徵態<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left\vert \uparrow \right\rangle }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>|</mo> <mo stretchy="false">↑</mo> <mo>⟩</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left\vert \uparrow \right\rangle }</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/40e620003115eac7fb280bc1dcc220a3b1598c43" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:2.714ex; height:2.843ex;" alt="{\displaystyle \left\vert \uparrow \right\rangle }">、<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left\vert \downarrow \right\rangle }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>|</mo> <mo stretchy="false">↓</mo> <mo>⟩</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left\vert \downarrow \right\rangle }</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1c8f6c3d8dddbe5bd4b229cd911f11c2f5e6daed" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:2.714ex; height:2.843ex;" alt="{\displaystyle \left\vert \downarrow \right\rangle }">，所以將量子算符<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\hat {S}}_{z}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>S</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>z</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\hat {S}}_{z}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7ac67cb8315ba14707385264d2f64e1e65a965f2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.574ex; height:3.176ex;" alt="{\displaystyle {\hat {S}}_{z}}">分別作用於這兩個本徵態，會得到<a href="#cite_note-Sakurai-21">[18]</a>:11-12 <dl><dd><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\hat {S}}_{z}\left\vert \uparrow \right\rangle =+{\tfrac {\hbar }{2}}\left\vert \uparrow \right\rangle }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>S</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>z</mi> </mrow> </msub> <mrow> <mo>|</mo> <mo stretchy="false">↑</mo> <mo>⟩</mo> </mrow> <mo>=</mo> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mfrac> <mi class="MJX-variant">ℏ</mi> <mn>2</mn> </mfrac> </mstyle> </mrow> <mrow> <mo>|</mo> <mo stretchy="false">↑</mo> <mo>⟩</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\hat {S}}_{z}\left\vert \uparrow \right\rangle =+{\tfrac {\hbar }{2}}\left\vert \uparrow \right\rangle }</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/232269237a12d5f956a84ad6f1059b66fc4e4e50" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:15.443ex; height:3.676ex;" alt="{\displaystyle {\hat {S}}_{z}\left\vert \uparrow \right\rangle =+{\tfrac {\hbar }{2}}\left\vert \uparrow \right\rangle }">、</dd> <dd><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\hat {S}}_{z}\left\vert \downarrow \right\rangle =-{\tfrac {\hbar }{2}}\left\vert \downarrow \right\rangle }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>S</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>z</mi> </mrow> </msub> <mrow> <mo>|</mo> <mo stretchy="false">↓</mo> <mo>⟩</mo> </mrow> <mo>=</mo> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mfrac> <mi class="MJX-variant">ℏ</mi> <mn>2</mn> </mfrac> </mstyle> </mrow> <mrow> <mo>|</mo> <mo stretchy="false">↓</mo> <mo>⟩</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\hat {S}}_{z}\left\vert \downarrow \right\rangle =-{\tfrac {\hbar }{2}}\left\vert \downarrow \right\rangle }</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6eb49b549e652813a4cf75e74a6c33a9f7142694" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:15.443ex; height:3.676ex;" alt="{\displaystyle {\hat {S}}_{z}\left\vert \downarrow \right\rangle =-{\tfrac {\hbar }{2}}\left\vert \downarrow \right\rangle }">。</dd></dl> 將量子算符<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\hat {S}}_{z}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>S</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>z</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\hat {S}}_{z}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7ac67cb8315ba14707385264d2f64e1e65a965f2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.574ex; height:3.176ex;" alt="{\displaystyle {\hat {S}}_{z}}">作用於量子態<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left\vert \psi \right\rangle =\alpha \left\vert \uparrow \right\rangle +\beta \left\vert \downarrow \right\rangle }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>|</mo> <mi>ψ</mi> <mo>⟩</mo> </mrow> <mo>=</mo> <mi>α</mi> <mrow> <mo>|</mo> <mo stretchy="false">↑</mo> <mo>⟩</mo> </mrow> <mo>+</mo> <mi>β</mi> <mrow> <mo>|</mo> <mo stretchy="false">↓</mo> <mo>⟩</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left\vert \psi \right\rangle =\alpha \left\vert \uparrow \right\rangle +\beta \left\vert \downarrow \right\rangle }</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d7bfac9b4220542cb3c794a35d8f4149e7520607" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:18.025ex; height:2.843ex;" alt="{\displaystyle \left\vert \psi \right\rangle =\alpha \left\vert \uparrow \right\rangle +\beta \left\vert \downarrow \right\rangle }">，會得到本徵值<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle +\hbar /2}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>+</mo> <mi class="MJX-variant">ℏ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle +\hbar /2}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/354b144f3a401ae92414a417e63197ef2b7b4a4b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:5.44ex; height:2.843ex;" alt="{\displaystyle +\hbar /2}">、<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle -\hbar /2}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>−</mo> <mi class="MJX-variant">ℏ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle -\hbar /2}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9e0bc5875fe0b0a5b3cb2fd489159c2c2156bfc1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:5.44ex; height:2.843ex;" alt="{\displaystyle -\hbar /2}">的概率分別為<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle |\alpha |^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>α</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle |\alpha |^{2}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fa34618537661f2d4d710cc26e8afe891f50f7b8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:3.836ex; height:3.343ex;" alt="{\displaystyle |\alpha |^{2}}">、<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle |\beta |^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>β</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle |\beta |^{2}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4caecb560883af3b9c0c3a1d0e13aae75f121d0d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:3.68ex; height:3.343ex;" alt="{\displaystyle |\beta |^{2}}">。假若本徵值為<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle +\hbar /2}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>+</mo> <mi class="MJX-variant">ℏ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle +\hbar /2}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/354b144f3a401ae92414a417e63197ef2b7b4a4b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:5.44ex; height:2.843ex;" alt="{\displaystyle +\hbar /2}">，則量子態<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left\vert \psi \right\rangle }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>|</mo> <mi>ψ</mi> <mo>⟩</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left\vert \psi \right\rangle }</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6e6a3a7d6221a16c2eff2d7ec038c3f8313a8240" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:3.065ex; height:2.843ex;" alt="{\displaystyle \left\vert \psi \right\rangle }">會塌縮為量子態<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left\vert \uparrow \right\rangle }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>|</mo> <mo stretchy="false">↑</mo> <mo>⟩</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left\vert \uparrow \right\rangle }</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/40e620003115eac7fb280bc1dcc220a3b1598c43" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:2.714ex; height:2.843ex;" alt="{\displaystyle \left\vert \uparrow \right\rangle }">；假若本徵值為<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle -\hbar /2}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>−</mo> <mi class="MJX-variant">ℏ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle -\hbar /2}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9e0bc5875fe0b0a5b3cb2fd489159c2c2156bfc1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:5.44ex; height:2.843ex;" alt="{\displaystyle -\hbar /2}">，則量子態<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left\vert \psi \right\rangle }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>|</mo> <mi>ψ</mi> <mo>⟩</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left\vert \psi \right\rangle }</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6e6a3a7d6221a16c2eff2d7ec038c3f8313a8240" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:3.065ex; height:2.843ex;" alt="{\displaystyle \left\vert \psi \right\rangle }">會塌縮為量子態<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left\vert \downarrow \right\rangle }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>|</mo> <mo stretchy="false">↓</mo> <mo>⟩</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left\vert \downarrow \right\rangle }</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1c8f6c3d8dddbe5bd4b229cd911f11c2f5e6daed" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:2.714ex; height:2.843ex;" alt="{\displaystyle \left\vert \downarrow \right\rangle }">。 <div class="mw-heading mw-heading3"><h3 id="动力学演化">动力学演化</h3>[<a href="/w/index.php?title=%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6&action=edit&section=9" title="编辑章节：动力学演化">编辑</a>]</div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r85100532"><div role="note" class="hatnote navigation-not-searchable">主条目：<a href="/wiki/%E9%87%8F%E5%AD%90%E8%89%B2%E5%8B%95%E5%8A%9B%E5%AD%B8" title="量子色動力學">量子色動力學</a>和<a href="/wiki/%E9%87%8F%E5%AD%90%E9%9B%BB%E5%8B%95%E5%8A%9B%E5%AD%B8" title="量子電動力學">量子電動力學</a></div> 在量子力學公設裏，第二項直接提到量子系統的動力學演化，其遵守含時薛丁格方程式，因此，量子態的演化在任意時刻可以被完全預測，具有連續性、命定性與可逆性。第四項提到，當對於量子系統作<a href="/wiki/%E9%87%8F%E5%AD%90%E6%B8%AC%E9%87%8F" title="量子測量">測量</a>時，其量子態會塌縮至幾個本徵態中的一個本徵態，具有不連續性、概率性與不可逆性。怎樣調和這兩種不同的行為，一種是關於量子態的自然演化，另一種是關於測量引發的演化，這仍舊是<a href="/wiki/%E6%9C%AA%E8%A7%A3%E6%B1%BA%E7%9A%84%E7%89%A9%E7%90%86%E5%AD%B8%E5%95%8F%E9%A1%8C" title="未解決的物理學問題">未解決的物理學問題</a>。<a href="#cite_note-Laloe-23">[20]</a>:7-11 量子系統的动力学演化可以用不同的绘景来表現。通过重新定义，这些不同的繪景可以互相變换，它们实际上是等價的。假若要專注分析量子態怎樣隨著時間的流易而演化，<a href="#時間演化算符">時間演化算符</a>怎樣影響量子態，則可採用<a href="/wiki/%E8%96%9B%E4%B8%81%E6%A0%BC%E7%B9%AA%E6%99%AF" title="薛丁格繪景">薛丁格繪景</a>。假若要專注了解對應於可觀察量的算符怎樣隨著時間的流易而演化、時間演化算符怎樣影響這些算符，則可採用<a href="/wiki/%E6%B5%B7%E6%A3%AE%E5%A0%A1%E7%BB%98%E6%99%AF" class="mw-redirect" title="海森堡绘景">海森堡绘景</a>。<a href="#cite_note-Sakurai-21">[18]</a>:80-89 <div class="mw-heading mw-heading2"><h2 id="主要論題">主要論題</h2>[<a href="/w/index.php?title=%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6&action=edit&section=10" title="编辑章节：主要論題">编辑</a>]</div> <div class="mw-heading mw-heading3"><h3 id="测量过程">测量过程</h3>[<a href="/w/index.php?title=%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6&action=edit&section=11" title="编辑章节：测量过程">编辑</a>]</div> 量子力学与經典力学的一个主要区别，在於怎樣理論論述测量过程。在經典力学裏，一个物理系统的位置和动量，可以同时被无限精确地确定和预測。在理论上，测量過程对物理系统本身，并不會造成任何影响，并可以无限精确地进行。在量子力学中则不然，测量过程本身会对系统造成影响。<a href="#cite_note-SEP_measurement-24">[21]</a> 怎樣才能正確地理論描述對於一个可观察量的测量？設定一个量子系统的量子态，首先，將量子態分解为该可观察量的一组本征态的线性组合。测量过程可以視為對於本征态的一个<a href="/wiki/%E6%8A%95%E5%BD%B1" class="mw-disambig" title="投影">投影</a>，测量结果是被投影的本征态的本征值。假設，按照某種程序製備出一個系綜，在這系綜裏，每一個量子態都與這量子態相同，現在對於這系綜裏的每一個量子態都進行一次測量，則可以获得所有可能的测量值（本徵值）的机率分布，每个测量值的概率等於量子態處於對應的本征态的<a href="/w/index.php?title=%E6%A6%82%E7%8E%87%E5%B9%85&action=edit&redlink=1" class="new" title="概率幅（页面不存在）">概率幅</a>的绝对值平方。<a href="#cite_note-Griffiths2004-22">[19]</a>:36-37, 96-100 因此，假設對於两个不同的可觀察量 <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7daff47fa58cdfd29dc333def748ff5fa4c923e3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle A}"> 和 <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle B}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>B</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle B}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/47136aad860d145f75f3eed3022df827cee94d7a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.764ex; height:2.176ex;" alt="{\displaystyle B}">做测量，改變測量顺序，例如從<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle AB}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mi>B</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle AB}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b04153f9681e5b06066357774475c04aaef3a8bd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.507ex; height:2.176ex;" alt="{\displaystyle AB}">改變為<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle BA}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>B</mi> <mi>A</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle BA}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5b8efb97e621ab9b49f8498a49704690bdeb2698" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.507ex; height:2.176ex;" alt="{\displaystyle BA}">，則可能直接影响测量结果。假若測量結果有所不同，則稱這兩個可觀察量為<a href="/wiki/%E4%B8%8D%E7%9B%B8%E5%AE%B9%E5%8F%AF%E8%A7%80%E5%AF%9F%E9%87%8F" class="mw-redirect" title="不相容可觀察量">不相容可觀察量</a>；否則，稱這兩個可觀察量為<a href="/wiki/%E4%B8%8D%E7%9B%B8%E5%AE%B9%E5%8F%AF%E8%A7%80%E5%AF%9F%E9%87%8F" class="mw-redirect" title="不相容可觀察量">相容可觀察量</a>。以數學術語表達，兩個不相容可觀察量<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7daff47fa58cdfd29dc333def748ff5fa4c923e3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle A}"> 和 <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle B}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>B</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle B}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/47136aad860d145f75f3eed3022df827cee94d7a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.764ex; height:2.176ex;" alt="{\displaystyle B}">的<a href="/wiki/%E5%B0%8D%E6%98%93%E7%AE%97%E7%AC%A6" class="mw-redirect" title="對易算符">對易算符</a>不等於零：<a href="#cite_note-Griffiths2004-22">[19]</a>:110-112 <dl><dd><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle [{\hat {A}},{\hat {B}}]\ {\stackrel {def}{=}}\ {\hat {A}}{\hat {B}}-{\hat {B}}{\hat {A}}\neq 0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">[</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>A</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>B</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mo stretchy="false">]</mo> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-REL"> <mover> <mrow class="MJX-TeXAtom-OP MJX-fixedlimits"> <mo>=</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>d</mi> <mi>e</mi> <mi>f</mi> </mrow> </mover> </mrow> </mrow> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>A</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>B</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>B</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>A</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mo>≠</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle [{\hat {A}},{\hat {B}}]\ {\stackrel {def}{=}}\ {\hat {A}}{\hat {B}}-{\hat {B}}{\hat {A}}\neq 0}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0961f37349e1bea9047ee6ae881fc590116ec249" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:23.739ex; height:4.009ex;" alt="{\displaystyle [{\hat {A}},{\hat {B}}]\ {\stackrel {def}{=}}\ {\hat {A}}{\hat {B}}-{\hat {B}}{\hat {A}}\neq 0}">。</dd></dl> <div class="mw-heading mw-heading3"><h3 id="不确定性原理">不确定性原理</h3>[<a href="/w/index.php?title=%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6&action=edit&section=12" title="编辑章节：不确定性原理">编辑</a>]</div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r85100532"><div role="note" class="hatnote navigation-not-searchable">主条目：<a href="/wiki/%E4%B8%8D%E7%A1%AE%E5%AE%9A%E6%80%A7%E5%8E%9F%E7%90%86" title="不确定性原理">不确定性原理</a></div> 不确定性原理表明，越能準確地設定粒子的位置，則越不能準確地設定粒子的動量，反之亦然，<a href="#cite_note-Hilgevoord_2016-25">[22]</a>:引言以方程式表示為<a href="#cite_note-Griffiths2004-22">[19]</a>:110-114 <dl><dd><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta x\Delta p\geq {\frac {\hbar }{2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <mi>x</mi> <mi mathvariant="normal">Δ</mi> <mi>p</mi> <mo>≥</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi class="MJX-variant">ℏ</mi> <mn>2</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta x\Delta p\geq {\frac {\hbar }{2}}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c4f31eda964ce0de251adeae4a2f43105ddc771c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:11.612ex; height:5.343ex;" alt="{\displaystyle \Delta x\Delta p\geq {\frac {\hbar }{2}}}">；</dd></dl> 其中，<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta x}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <mi>x</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta x}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f3890eb866b6258d7a304fc34c70ee3fb3a81a70" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.266ex; height:2.176ex;" alt="{\displaystyle \Delta x}">、<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta p}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <mi>p</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta p}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0758c326125ad3d8b96e515c7fd69164ec587b81" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.105ex; height:2.509ex;" alt="{\displaystyle \Delta p}">分別為位置、動量的不確定性。 設想一個定域性的<a href="/wiki/%E6%B3%A2%E5%8C%85" title="波包">波包</a>，假設波包的尺寸為<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle L}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>L</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle L}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/103168b86f781fe6e9a4a87b8ea1cebe0ad4ede8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.583ex; height:2.176ex;" alt="{\displaystyle L}"> ．從計數波包的<a href="/wiki/%E9%80%B1%E6%9C%9F" title="週期">週期</a>數<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle N}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>N</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle N}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f5e3890c981ae85503089652feb48b191b57aae3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.064ex; height:2.176ex;" alt="{\displaystyle N}">，可以知道其波數<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle k}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>k</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle k}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c3c9a2c7b599b37105512c5d570edc034056dd40" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.211ex; height:2.176ex;" alt="{\displaystyle k}">： <dl><dd><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle k=2\pi N/L}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>k</mi> <mo>=</mo> <mn>2</mn> <mi>π</mi> <mi>N</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>L</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle k=2\pi N/L}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5fd9f242850801c1f79441fc0785717f01723924" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:11.613ex; height:2.843ex;" alt="{\displaystyle k=2\pi N/L}">。</dd></dl> 假若，計數<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle N}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>N</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle N}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f5e3890c981ae85503089652feb48b191b57aae3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.064ex; height:2.176ex;" alt="{\displaystyle N}">的不確定性為<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta N=1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <mi>N</mi> <mo>=</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta N=1}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f3a82310ccca61471e74205f42729c1ba29baaea" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:8.26ex; height:2.176ex;" alt="{\displaystyle \Delta N=1}">，那麼，<a href="/wiki/%E6%B3%A2%E6%95%B8" title="波數">波數</a>的不確定性是 <dl><dd><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta k=2\pi /L}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <mi>k</mi> <mo>=</mo> <mn>2</mn> <mi>π</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>L</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta k=2\pi /L}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/de8f9a4be34955134ca66a0130f9ad20b1de6599" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:11.485ex; height:2.843ex;" alt="{\displaystyle \Delta k=2\pi /L}">。</dd></dl> 根據<a href="/wiki/%E5%BE%B7%E5%B8%83%E7%BE%85%E6%84%8F%E5%81%87%E8%AA%AA" class="mw-redirect" title="德布羅意假說">德布羅意假說</a>，<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle P=\hbar k}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>P</mi> <mo>=</mo> <mi class="MJX-variant">ℏ</mi> <mi>k</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P=\hbar k}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/32795c43d69d21fc18e88721b72c1eca8b494ac2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:7.362ex; height:2.176ex;" alt="{\displaystyle P=\hbar k}">。因此，動量的不確定性是 <dl><dd><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta P=\hbar \Delta k={\frac {h}{L}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <mi>P</mi> <mo>=</mo> <mi class="MJX-variant">ℏ</mi> <mi mathvariant="normal">Δ</mi> <mi>k</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>h</mi> <mi>L</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta P=\hbar \Delta k={\frac {h}{L}}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2dbd72491825bc14a9f7c826baeea6dd674c37d0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:16.751ex; height:5.343ex;" alt="{\displaystyle \Delta P=\hbar \Delta k={\frac {h}{L}}}">。</dd></dl> 由於粒子位置的不確定性是<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta X\approx L/2}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <mi>X</mi> <mo>≈</mo> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta X\approx L/2}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b7f0d20d52b366d82ce17b6b10555ff1df4d75c1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:10.922ex; height:2.843ex;" alt="{\displaystyle \Delta X\approx L/2}">，所以，這兩個不相容可觀察量的不確定性為<a href="#cite_note-Braginsky1995-26">[23]</a>:5-6 <dl><dd><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta P\Delta X\approx h/2}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <mi>P</mi> <mi mathvariant="normal">Δ</mi> <mi>X</mi> <mo>≈</mo> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta P\Delta X\approx h/2}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c7b85fe7533fdc4be782d3dda5fe4ce4a058a5a9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:14.36ex; height:2.843ex;" alt="{\displaystyle \Delta P\Delta X\approx h/2}">。</dd></dl> <div class="mw-heading mw-heading3"><h3 id="全同粒子">全同粒子</h3>[<a href="/w/index.php?title=%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6&action=edit&section=13" title="编辑章节：全同粒子">编辑</a>]</div> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Asymmetricwave2.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/0d/Asymmetricwave2.png/200px-Asymmetricwave2.png" decoding="async" width="200" height="150" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/0d/Asymmetricwave2.png/300px-Asymmetricwave2.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/0d/Asymmetricwave2.png/400px-Asymmetricwave2.png 2x" data-file-width="1814" data-file-height="1358" /></a><figcaption>在<a href="/wiki/%E7%84%A1%E9%99%90%E6%B7%B1%E6%96%B9%E5%BD%A2%E9%98%B1" title="無限深方形阱">無限深方形阱</a>裏，兩個全同費米子的反對稱性波函數繪圖。<a href="#cite_note-27">[d]</a></figcaption></figure> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Symmetricwave2.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/1d/Symmetricwave2.png/200px-Symmetricwave2.png" decoding="async" width="200" height="150" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/1d/Symmetricwave2.png/300px-Symmetricwave2.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/1d/Symmetricwave2.png/400px-Symmetricwave2.png 2x" data-file-width="1811" data-file-height="1356" /></a><figcaption>在<a href="/wiki/%E7%84%A1%E9%99%90%E6%B7%B1%E6%96%B9%E5%BD%A2%E9%98%B1" title="無限深方形阱">無限深方形阱</a>裏，兩個全同玻色子的對稱波函數繪圖。<a href="#cite_note-28">[e]</a></figcaption></figure> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r85100532"><div role="note" class="hatnote navigation-not-searchable">主条目：<a href="/wiki/%E5%85%A8%E5%90%8C%E7%B2%92%E5%AD%90" title="全同粒子">全同粒子</a>和<a href="/wiki/%E5%8C%85%E7%AB%8B%E4%B8%8D%E7%9B%B8%E5%AE%B9%E5%8E%9F%E7%90%86" class="mw-redirect" title="包立不相容原理">包立不相容原理</a></div> 粒子具有很多種物理性質，例如<a href="/wiki/%E8%B3%AA%E9%87%8F" class="mw-redirect" title="質量">質量</a>、<a href="/wiki/%E9%9B%BB%E8%8D%B7" title="電荷">電荷</a>、<a href="/wiki/%E8%87%AA%E6%97%8B" title="自旋">自旋</a>等等。假若兩個粒子具有不同的性質，則可以藉著測量這些不同的性質來區分這兩個粒子。根據許多實驗獲得的結果，同種類的粒子具有完全相同的性質，例如，宇宙裏所有的電子都帶有相等數量的電荷。因此，無法依靠物理性質來區分同種類的粒子，必須使用另一種區分法，即跟蹤每一個粒子的軌道。只要能夠無限精確地測量出每一個粒子的位置，就不會搞不清楚哪一個粒子在哪裡。這個適用於經典力學的方法有一個問題，那就是它與量子力學的基本原理相矛盾。根據量子理論，在位置測量期間，粒子不會保持明確的位置。粒子的位置具有<a href="/w/index.php?title=%E6%A6%82%E7%8E%87%E6%80%A7&action=edit&redlink=1" class="new" title="概率性（页面不存在）">概率性</a>。隨著時間的流易，幾個粒子的量子態可能會移動蔓延，因此某些部分會互相重疊在一起。假若發生重疊事件，给每个粒子“挂上一个标签”的方法立刻失去了意义，就無法區分在重疊區域的兩個粒子。<a href="#cite_note-Griffiths2004-22">[19]</a>:201ff <a href="/wiki/%E5%85%A8%E5%90%8C%E7%B2%92%E5%AD%90" title="全同粒子">全同粒子</a>所呈現出的不可区分性，对量子态的<a href="/wiki/%E5%AF%B9%E7%A7%B0%E6%80%A7" class="mw-redirect" title="对称性">对称性</a>，以及多粒子系统的<a href="/wiki/%E7%BB%9F%E8%AE%A1%E5%8A%9B%E5%AD%A6" title="统计力学">统计力学</a>，有深远的影响。比如说，一个由全同粒子组成的多粒子系统量子态，在交换两个粒子“1”和粒子“2”时，可以证明，不是对称的 <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle (|\psi _{12}\rangle =+|\psi _{21}\rangle )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <msub> <mi>ψ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>12</mn> </mrow> </msub> <mo fence="false" stretchy="false">⟩</mo> <mo>=</mo> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <msub> <mi>ψ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>21</mn> </mrow> </msub> <mo fence="false" stretchy="false">⟩</mo> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (|\psi _{12}\rangle =+|\psi _{21}\rangle )}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3746d67db042414e668538d16ade01bf1d976a7b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:16.598ex; height:2.843ex;" alt="{\displaystyle (|\psi _{12}\rangle =+|\psi _{21}\rangle )}"> ，就是反对称的 <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle (|\psi _{12}\rangle =-|\psi _{21}\rangle )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <msub> <mi>ψ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>12</mn> </mrow> </msub> <mo fence="false" stretchy="false">⟩</mo> <mo>=</mo> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <msub> <mi>ψ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>21</mn> </mrow> </msub> <mo fence="false" stretchy="false">⟩</mo> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (|\psi _{12}\rangle =-|\psi _{21}\rangle )}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6ee88b021ca22d9c02017d924c3740096220eb9e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:16.598ex; height:2.843ex;" alt="{\displaystyle (|\psi _{12}\rangle =-|\psi _{21}\rangle )}"> 。具有对称性的粒子被称为<a href="/wiki/%E7%8E%BB%E8%89%B2%E5%AD%90" title="玻色子">玻色子</a>，具有反对称性的粒子被称为<a href="/wiki/%E8%B4%B9%E7%B1%B3%E5%AD%90" title="费米子">费米子</a>。此外<a href="/wiki/%E8%87%AA%E6%97%8B" title="自旋">自旋</a>的对换也形成对称：自旋为半数的粒子（如电子、<a href="/wiki/%E8%B3%AA%E5%AD%90" title="質子">质子</a>和<a href="/wiki/%E4%B8%AD%E5%AD%90" title="中子">中子</a>）是反对称的，因此是费米子；自旋为整数的粒子（如光子）是对称的，因此是玻色子。 由於费米子系統具有反对称性，費米子遵守<a href="/wiki/%E6%B3%A1%E5%88%A9%E4%B8%8D%E7%9B%B8%E5%AE%B9%E5%8E%9F%E7%90%86" title="泡利不相容原理">泡利不相容原理</a>，即两个费米子无法占据同一状态<a href="#cite_note-Sakurai-21">[18]</a>:451。这个原理拥有极大的实用意义。它表明，在由原子组成的物质世界裡，电子无法同时占据同一状态，因此在最低状态被占据後，下一个电子必须占据次低的状态，直到所有的状态均被满足为止。这个现象决定了物质的物理和化学特性<a href="#cite_note-Griffiths2004-22">[19]</a>:204,214,218-221。 费米子与玻色子的状态的热分布也相差很大：玻色子遵循<a href="/wiki/%E7%8E%BB%E8%89%B2-%E7%88%B1%E5%9B%A0%E6%96%AF%E5%9D%A6%E7%BB%9F%E8%AE%A1" class="mw-redirect" title="玻色-爱因斯坦统计">玻色-爱因斯坦统计</a>，而费米子则遵循<a href="/wiki/%E8%B4%B9%E7%B1%B3-%E7%8B%84%E6%8B%89%E5%85%8B%E7%BB%9F%E8%AE%A1" title="费米-狄拉克统计">费米-狄拉克统计</a><a href="#cite_note-Sakurai-21">[18]</a>:450。 <div class="mw-heading mw-heading3"><h3 id="量子纠缠">量子纠缠</h3>[<a href="/w/index.php?title=%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6&action=edit&section=14" title="编辑章节：量子纠缠">编辑</a>]</div> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:EPR-Experiment_Bohm_1676x516_zh.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a6/EPR-Experiment_Bohm_1676x516_zh.png/350px-EPR-Experiment_Bohm_1676x516_zh.png" decoding="async" width="350" height="101" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a6/EPR-Experiment_Bohm_1676x516_zh.png/525px-EPR-Experiment_Bohm_1676x516_zh.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a6/EPR-Experiment_Bohm_1676x516_zh.png/700px-EPR-Experiment_Bohm_1676x516_zh.png 2x" data-file-width="1680" data-file-height="485" /></a><figcaption>假設一個零自旋中性<a href="/wiki/%CE%A0%E4%BB%8B%E5%AD%90" title="Π介子">π介子</a>衰變成一個<a href="/wiki/%E9%9B%BB%E5%AD%90" class="mw-redirect" title="電子">電子</a>與一個<a href="/wiki/%E6%AD%A3%E9%9B%BB%E5%AD%90" title="正電子">正電子</a>，這兩個衰變產物各自朝著相反方向移動，雖然彼此之間相隔一段距離，它們仍舊會發生量子糾纏現象。</figcaption></figure> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r85100532"><div role="note" class="hatnote navigation-not-searchable">主条目：<a href="/wiki/%E9%87%8F%E5%AD%90%E7%BA%A0%E7%BC%A0" class="mw-redirect" title="量子纠缠">量子纠缠</a></div> 假設兩個粒子在經過短暫時間彼此耦合之後，單獨攪擾其中任意一個粒子，儘管兩個粒子之間可能相隔很長一段距離，還是會不可避免地影響到另外一個粒子的性質，這種關聯現象稱為量子糾纏。往往由多个粒子组成的量子系统，其状态无法被分离为其组成的单个粒子的状态，在这种情况下，单个粒子的状态被称为是纠缠的。纠缠的粒子有惊人的特性，这些特性违背一般的直觉。比如说，对一个粒子的测量，可以导致整个系统的波包立刻塌缩，因此也影响到另一个、遥远的、与被测量的粒子纠缠的粒子。这个现象并不违背<a href="/wiki/%E7%8B%AD%E4%B9%89%E7%9B%B8%E5%AF%B9%E8%AE%BA" title="狭义相对论">狭义相对论</a>，因为在量子力学的层面上，在测量粒子前，它们不能被單獨各自定义，实际上它们仍是一个整体。不过在测量它们之后，它们就会脱离量子纠缠的状态。<a href="#cite_note-Laloe-23">[20]</a>:27-31:120ff <div class="mw-heading mw-heading3"><h3 id="量子退相干">量子退相干</h3>[<a href="/w/index.php?title=%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6&action=edit&section=15" title="编辑章节：量子退相干">编辑</a>]</div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r85100532"><div role="note" class="hatnote navigation-not-searchable">主条目：<a href="/wiki/%E9%87%8F%E5%AD%90%E9%80%80%E7%9B%B8%E5%B9%B2" title="量子退相干">量子退相干</a></div> 作为一个基本理论，量子力学原则上，应该适用于任何大小的物理系统，也就是说不仅限于<a href="/wiki/%E5%AE%8F%E8%A7%82" title="宏观">微观系统</a>，那么，它应该提供一个过渡到<a href="/wiki/%E5%AE%8F%E8%A7%82" title="宏观">宏观</a>經典物理的方法。量子现象的存在提出了一个问题，即怎样从量子力学的观点，解释宏观系统的經典现象。尤其无法直接看出的是，量子力学中的<a href="/wiki/%E9%87%8F%E5%AD%90%E7%96%8A%E5%8A%A0" class="mw-redirect" title="量子疊加">量子疊加</a>，在宏观世界怎樣呈現出來。1954年，爱因斯坦在给<a href="/wiki/%E9%A9%AC%E5%85%8B%E6%96%AF%C2%B7%E7%8E%BB%E6%81%A9" title="马克斯·玻恩">马克斯·玻恩</a>的信中，就提出了怎样从量子力学的角度，来解释宏观世界的物理現象的问题，他指出仅仅量子力学现象太“小”无法解释这个问题。<a href="#cite_note-Joos2003-29">[24]</a>:62-63这个问题的另一个例子是由薛定谔提出的<a href="/wiki/%E8%96%9B%E5%AE%9A%E8%B0%94%E7%8C%AB" title="薛定谔猫">薛定谔猫</a>的思想实验。<a href="#cite_note-Joos2003-29">[24]</a>:2 後來，物理學者领会到，上述的思想实验，实际而言并不合乎現實，因为它们忽略了不可避免地与周围环境的相互作用，量子系統會因為這相互作用與環境<a href="/wiki/%E9%97%9C%E8%81%AF" class="mw-redirect" title="關聯">關聯</a>在一起。處於<a href="/wiki/%E9%87%8F%E5%AD%90%E7%96%8A%E5%8A%A0" class="mw-redirect" title="量子疊加">疊加態</a>的量子系統非常容易受周围环境的影响，而且隨著時間流逝，這量子系統會與環境永無休止地越加深入<a href="/wiki/%E9%87%8F%E5%AD%90%E7%BA%A0%E7%BC%A0" class="mw-redirect" title="量子纠缠">糾纏</a>，這現象稱為「馮紐曼無窮鏈」（Von Neumann's infinite chain）。在疊加態裏，幾個相互正交的量子態疊加在一起，彼此相干。量子退相干是一種過程，能夠將量子系統的<a href="/wiki/%E5%AF%86%E5%BA%A6%E7%9F%A9%E9%99%A3" title="密度矩陣">約化密度矩陣</a>對角化，而相干性質就是表示於這約化密度矩陣的非對角元素，所以，疊加態的相干性質會快速消失，無法再被探測到，從而呈現出經典的統計性質。雖然量子系統的疊加態不再具有相干性質，整個量子系統與環境共同組成的聯合態仍舊具有相干性質。<a href="#cite_note-Laloe-23">[20]</a>:19-21, 136-138<a href="#cite_note-Schlosshauer2004-30">[25]</a> 对于<a href="/wiki/%E9%87%8F%E5%AD%90%E8%AE%A1%E7%AE%97%E6%9C%BA" title="量子计算机">量子计算机</a>来说，量子退相干也有实际意义。在一台量子计算机中，需要多个量子状态尽可能地长时间保持叠加。退相干时间短是一个非常大的技术问题，因為它會削弱量子疊加效應，但它也是一個必需的因素，因為儲存在計算機內的數據必需經過量子測量被讀出來。<a href="#cite_note-31">[26]</a> <div class="mw-heading mw-heading2"><h2 id="与其它物理理论的关系">与其它物理理论的关系</h2>[<a href="/w/index.php?title=%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6&action=edit&section=16" title="编辑章节：与其它物理理论的关系">编辑</a>]</div> <div class="mw-heading mw-heading3"><h3 id="經典物理">經典物理</h3>[<a href="/w/index.php?title=%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6&action=edit&section=17" title="编辑章节：經典物理">编辑</a>]</div> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Hamilton_analogy_zh-hans.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/46/Hamilton_analogy_zh-hans.svg/200px-Hamilton_analogy_zh-hans.svg.png" decoding="async" width="200" height="116" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/46/Hamilton_analogy_zh-hans.svg/300px-Hamilton_analogy_zh-hans.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/46/Hamilton_analogy_zh-hans.svg/400px-Hamilton_analogy_zh-hans.svg.png 2x" data-file-width="450" data-file-height="260" /></a><figcaption>波動光學在短波長極限成為幾何光學，類似地，量子力學在普朗克常數趨零極限成為經典力學。基本而言，在<a href="/wiki/%E6%99%AE%E6%9C%97%E5%85%8B%E5%B8%B8%E6%95%B8" class="mw-redirect" title="普朗克常數">普朗克常數</a>趨零極限，可以從量子力學的<a href="/wiki/%E8%96%9B%E4%B8%81%E6%A0%BC%E6%96%B9%E7%A8%8B%E5%BC%8F" class="mw-redirect" title="薛丁格方程式">薛丁格方程式</a>推導出經典力學的<a href="/wiki/%E5%93%88%E5%AF%86%E9%A0%93-%E4%BA%9E%E5%8F%AF%E6%AF%94%E6%96%B9%E7%A8%8B%E5%BC%8F" class="mw-redirect" title="哈密頓-亞可比方程式">哈密頓-亞可比方程式</a>。詳盡細節，請參閱條目<a href="/wiki/%E5%93%88%E5%AF%86%E9%A1%BF%EF%BC%8D%E9%9B%85%E5%8F%AF%E6%AF%94%E6%96%B9%E7%A8%8B#波動方程式⇒粒子方程式" class="mw-redirect" title="哈密顿－雅可比方程">哈密頓-亞可比方程式</a>。<a href="#cite_note-Joas-32">[27]</a></figcaption></figure> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r85100532"><div role="note" class="hatnote navigation-not-searchable">主条目：<a href="/wiki/%E7%B6%93%E5%85%B8%E7%89%A9%E7%90%86" class="mw-redirect" title="經典物理">經典物理</a>和<a href="/wiki/%E5%8D%8A%E7%B6%93%E5%85%B8%E7%89%A9%E7%90%86%E5%AD%B8" title="半經典物理學">半經典物理學</a></div> 量子力學的預測已被實驗核對至極高準確度，是在科學領域中，最為準確的理論之一。<a href="#cite_note-Hobson-11">[10]</a><a href="/wiki/%E5%B0%8D%E6%87%89%E5%8E%9F%E7%90%86" class="mw-redirect" title="對應原理">對應原理</a>實現經典力學與量子力學之間的對應關係，根據對應原理，假若量子系统已達到某「經典極限」，則其物理行為可以很精确地用經典理论來描述；這經典極限可以是大<a href="/wiki/%E9%87%8F%E5%AD%90%E6%95%B8" class="mw-redirect" title="量子數">量子數</a>極限，也可以是<a href="/wiki/%E6%99%AE%E6%9C%97%E5%85%8B%E5%B8%B8%E6%95%B8" class="mw-redirect" title="普朗克常數">普朗克常數</a>趨零極限。實際而言，许多宏观系统都是用經典理论（如經典力学和电磁学）来做精确描述。因此在非常“大”的系统中，量子力学的特性應該会逐漸與經典物理的特性相近似，两者必須相互符合。<a href="#cite_note-Muynck2002-33">[28]</a>:190-191 对应原理對於建立一个有效的量子力学模型是很重要的辅助工具。量子力学的数学基础相當廣泛寬鬆，它僅只要求量子系統的態向量屬於<a href="/wiki/%E5%B8%8C%E5%B0%94%E4%BC%AF%E7%89%B9%E7%A9%BA%E9%97%B4" title="希尔伯特空间">希尔伯特空间</a>，其<a href="/wiki/%E5%8F%AF%E8%A7%82%E5%AF%9F%E9%87%8F" class="mw-redirect" title="可观察量">可观察量</a>是线性的<a href="/wiki/%E5%8E%84%E7%B1%B3%E7%AE%97%E7%AC%A6" class="mw-redirect" title="厄米算符">厄米算符</a>，它并没有规定在实际情况下，应该选择哪一种希尔伯特空间、哪些厄米算符。因此，在实际情况下，必须选择相应的希尔伯特空间和算符来描写一个特定的量子系统。而对应原理则是做出这个选择的一个重要辅助工具。这个原理要求量子力学所做出的预言，在越来越大的系统中，逐渐近似經典理论的预言。这个大系统的极限，被称为“經典极限”或者“对应极限”。因此可以使用<a href="/wiki/%E5%90%AF%E5%8F%91%E6%B3%95" title="启发法">启发法</a>的手段，来建立一个量子力学的模型，而这个模型的极限，就是相应的經典物理学的模型。<a href="#cite_note-Muynck2002-33">[28]</a>:190-191<a href="#cite_note-Nielsen1976-34">[29]</a>:3ff 在經典系統與量子系統之間，<a href="/wiki/%E7%9B%B8%E5%B9%B2%E6%80%A7#量子相干性" title="相干性">量子相干</a>是一種很明顯可以用來區分的性質，具有量子相干性的電子、光子等等微觀粒子可以處於量子疊加態，不具有量子相干性的棒球、老虎等等宏觀系統不可以處於量子疊加態。<a href="/wiki/%E9%87%8F%E5%AD%90%E9%80%80%E7%9B%B8%E5%B9%B2" title="量子退相干">量子退相干</a>可以用來解釋這些行為。一種應用這性質來區分的工具是<a href="/wiki/%E8%B4%9D%E5%B0%94%E4%B8%8D%E7%AD%89%E5%BC%8F" class="mw-redirect" title="贝尔不等式">貝爾不等式</a>，遭到量子糾纏的系統不遵守貝爾不等式，而量子退相干能夠將量子糾纏性質變換為經典統計性質，系統的物理行為因此可以用<a href="/wiki/%E9%9A%B1%E8%AE%8A%E6%95%B8%E7%90%86%E8%AB%96" class="mw-redirect" title="隱變數理論">隱變數理論</a>解釋，不再不遵守貝爾不等式。<a href="#cite_note-Haroche-35">[30]</a>:80-82簡略而言，量子干涉是將幾個量子態的<a href="/wiki/%E9%87%8F%E5%AD%90%E5%B9%85" class="mw-redirect" title="量子幅">量子幅</a>總和在一起，而經典干涉則是將幾個經典波動的<a href="/wiki/%E6%B3%A2" title="波">波強</a>總和在一起。對於微觀物體，整個系統的延伸尺寸超小於<a href="/wiki/%E7%9B%B8%E5%B9%B2%E6%80%A7" title="相干性">相干長度</a>，因此會產生長程<a href="/wiki/%E9%87%8F%E5%AD%90%E7%BA%A0%E7%BC%A0" class="mw-redirect" title="量子纠缠">量子糾纏</a>與其它非定域現象，一些量子系統的特徵行為。通常，量子相干不會出現於宏觀系統。<a href="#cite_note-36">[31]</a> <div class="mw-heading mw-heading3"><h3 id="狹義相对论">狹義相对论</h3>[<a href="/w/index.php?title=%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6&action=edit&section=18" title="编辑章节：狹義相对论">编辑</a>]</div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r85100532"><div role="note" class="hatnote navigation-not-searchable">主条目：<a href="/wiki/%E7%8B%B9%E7%BE%A9%E7%9B%B8%E5%B0%8D%E8%AB%96" class="mw-redirect" title="狹義相對論">狹義相對論</a></div> 原本量子力學的表述所針對的模型，其對應極限為非相對論性古典力學。例如，眾所皆知的<a href="/wiki/%E9%87%8F%E5%AD%90%E8%AB%A7%E6%8C%AF%E5%AD%90" title="量子諧振子">量子諧振子</a>模型使用了非相對論性表達式來表達其<a href="/wiki/%E5%8B%95%E8%83%BD" class="mw-redirect" title="動能">動能</a>，因此，這模型是<a href="/wiki/%E8%AB%A7%E6%8C%AF%E5%AD%90" title="諧振子">古典諧振子</a>的量子版本。<a href="#cite_note-Griffiths2004-22">[19]</a>:40-59 早期，對於合併量子力学与<a href="/wiki/%E7%8B%AD%E4%B9%89%E7%9B%B8%E5%AF%B9%E8%AE%BA" title="狭义相对论">狭义相对论</a>的试图，涉及到使用<a href="/wiki/%E5%8D%8F%E5%8F%98" class="mw-redirect mw-disambig" title="协变">協變方程式</a>，例如，<a href="/wiki/%E5%85%8B%E8%8E%B1%E5%9B%A0-%E6%88%88%E5%B0%94%E7%99%BB%E6%96%B9%E7%A8%8B" title="克莱因-戈尔登方程">克莱因-戈尔登方程</a>或<a href="/wiki/%E7%8B%84%E6%8B%89%E5%85%8B%E6%96%B9%E7%A8%8B%E5%BC%8F" title="狄拉克方程式">狄拉克方程式</a>，来取代薛定谔方程。这些方程雖然能夠很成功地描述许多量子现象，但它们目有某些不滿意的問題，它们无法描述在相对论性状況下，粒子的生成和湮滅。完整的<a href="/wiki/%E9%87%8F%E5%AD%90%E5%9C%BA%E8%AE%BA" title="量子场论">相对论性量子理论</a>需要<a href="/wiki/%E9%87%8F%E5%AD%90%E5%9C%BA%E8%AE%BA" title="量子场论">量子场论</a>的關鍵发展。量子场论能夠将<a href="/wiki/%E5%A0%B4_(%E7%89%A9%E7%90%86)" class="mw-redirect" title="場 (物理)">场</a>量子化（而不是一組固定數量的粒子）。第一个量子场论是<a href="/wiki/%E9%87%8F%E5%AD%90%E7%94%B5%E5%8A%A8%E5%8A%9B%E5%AD%A6" class="mw-redirect" title="量子电动力学">量子电动力学</a>，它可以精確地描写<a href="/wiki/%E7%94%B5%E7%A3%81%E7%9B%B8%E4%BA%92%E4%BD%9C%E7%94%A8" class="mw-redirect" title="电磁相互作用">电磁相互作用</a>。<a href="#cite_note-Sakurai-21">[18]</a>:486-514<a href="/wiki/%E9%87%8F%E5%AD%90%E9%9B%BB%E5%8B%95%E5%8A%9B%E5%AD%B8" title="量子電動力學">量子電動力學</a>其對於某些原子性質的理論預測，已被證實準確至108分之一。<a href="#cite_note-feynbook-37">[32]</a>:7 對於描述电磁系统，時常不需要使用到量子场论的全部功能。比较简单的方法，是将带电粒子当作处於經典电磁场中的量子力学物体。这个手段从量子力学的初期，就已经被使用了。比如说，<a href="/wiki/%E6%B0%A2%E5%8E%9F%E5%AD%90" class="mw-redirect" title="氢原子">氢原子</a>的电子状态，可以近似地使用經典的 <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 1/r}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>r</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 1/r}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2ab96580d23ec5eff6bb0e666531eccb7a8035d6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:3.374ex; height:2.843ex;" alt="{\displaystyle 1/r}"> 庫侖勢来计算。这就是所谓的半經典方法。但是，在电磁场中的量子起伏起一个重要作用的情况下（比如带电粒子发射一颗光子）这个近似方法就失效了。<a href="#cite_note-Griffiths2004-22">[19]</a>:145-160 <div class="mw-heading mw-heading3"><h3 id="粒子物理學">粒子物理學</h3>[<a href="/w/index.php?title=%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6&action=edit&section=19" title="编辑章节：粒子物理學">编辑</a>]</div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r85100532"><div role="note" class="hatnote navigation-not-searchable">主条目：<a href="/wiki/%E5%BC%B7%E7%9B%B8%E4%BA%92%E4%BD%9C%E7%94%A8" class="mw-redirect" title="強相互作用">強相互作用</a>和<a href="/wiki/%E5%BC%B1%E7%9B%B8%E4%BA%92%E4%BD%9C%E7%94%A8" title="弱相互作用">弱相互作用</a></div> 專門描述<a href="/wiki/%E5%BC%BA%E7%9B%B8%E4%BA%92%E4%BD%9C%E7%94%A8" title="强相互作用">强相互作用</a>、<a href="/wiki/%E5%BC%B1%E7%9B%B8%E4%BA%92%E4%BD%9C%E7%94%A8" title="弱相互作用">弱相互作用</a>的量子場論已發展成功。<a href="/wiki/%E5%BC%BA%E7%9B%B8%E4%BA%92%E4%BD%9C%E7%94%A8" title="强相互作用">强相互作用</a>的量子场论稱為<a href="/wiki/%E9%87%8F%E5%AD%90%E8%89%B2%E5%8A%A8%E5%8A%9B%E5%AD%A6" class="mw-redirect" title="量子色动力学">量子色动力学</a>，这个理论描述亞原子粒子，例如<a href="/wiki/%E5%A4%B8%E5%85%8B" title="夸克">夸克</a>、<a href="/wiki/%E8%86%A0%E5%AD%90" title="膠子">胶子</a>，它們彼此之间的相互作用。<a href="/wiki/%E5%BC%B1%E7%9B%B8%E4%BA%92%E4%BD%9C%E7%94%A8" title="弱相互作用">弱相互作用</a>与<a href="/wiki/%E7%94%B5%E7%A3%81%E7%9B%B8%E4%BA%92%E4%BD%9C%E7%94%A8" class="mw-redirect" title="电磁相互作用">电磁相互作用</a>也被統一為單獨量子場論，稱為<a href="/wiki/%E7%94%B5%E5%BC%B1%E7%9B%B8%E4%BA%92%E4%BD%9C%E7%94%A8" class="mw-redirect" title="电弱相互作用">电弱相互作用</a>。<a href="#cite_note-Halliday-8">[7]</a>:1234-1236 <div class="mw-heading mw-heading3"><h3 id="廣義相對論">廣義相對論</h3>[<a href="/w/index.php?title=%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6&action=edit&section=20" title="编辑章节：廣義相對論">编辑</a>]</div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r85100532"><div role="note" class="hatnote navigation-not-searchable">主条目：<a href="/wiki/%E9%87%8F%E5%AD%90%E5%BC%95%E5%8A%9B" title="量子引力">量子引力</a>和<a href="/wiki/%E5%BB%A3%E7%BE%A9%E7%9B%B8%E5%B0%8D%E8%AB%96" title="廣義相對論">廣義相對論</a></div> <a href="/wiki/%E9%87%8F%E5%AD%90%E5%BC%95%E5%8A%9B" title="量子引力">量子引力</a>是對<a href="/wiki/%E5%BC%95%E5%8A%9B%E5%A0%B4" title="引力場">引力場</a>進行量子化描述的理論，屬於<a href="/wiki/%E8%90%AC%E6%9C%89%E7%90%86%E8%AB%96" class="mw-redirect" title="萬有理論">萬有理論</a>之一。物理學者發覺，建造引力的量子模型是一件非常艱難的研究。半經典近似是一種可行方法，推導出一些很有意思的預測，例如，<a href="/wiki/%E9%9C%8D%E9%87%91%E8%BC%BB%E5%B0%84" title="霍金輻射">霍金輻射</a>等等。可是，由於<a href="/wiki/%E5%BB%A3%E7%BE%A9%E7%9B%B8%E5%B0%8D%E8%AB%96" title="廣義相對論">廣義相對論</a>（至今為止，最成功的引力理論）與量子力學的一些基礎假說相互矛盾，表述出一個完整的量子引力理論遭到了嚴峻阻礙。嘗試結合<a href="/wiki/%E5%BB%A3%E7%BE%A9%E7%9B%B8%E5%B0%8D%E8%AB%96" title="廣義相對論">廣義相對論</a>與<a href="/wiki/%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%B8" class="mw-redirect" title="量子力學">量子力學</a>是熱門研究方向，為當前的物理學尚未解决的問題。當前主流嘗試理論有：<a href="/wiki/%E8%B6%85%E5%BC%A6%E7%90%86%E8%AB%96" title="超弦理論">超弦理論</a>、<a href="/wiki/%E8%BF%B4%E5%9C%88%E9%87%8F%E5%AD%90%E9%87%8D%E5%8A%9B%E7%90%86%E8%AB%96" class="mw-redirect" title="迴圈量子重力理論">迴圈量子重力理論</a>等等。<a href="#cite_note-38">[33]</a><a href="#cite_note-39">[34]</a> <div class="mw-heading mw-heading2"><h2 id="哲学观点">哲学观点</h2>[<a href="/w/index.php?title=%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6&action=edit&section=21" title="编辑章节：哲学观点">编辑</a>]</div> <style data-mw-deduplicate="TemplateStyles:r82655521">.mw-parser-output .side-box{margin:4px 0;box-sizing:border-box;border:1px solid #aaa;font-size:88%;line-height:1.25em;background-color:#f9f9f9;display:flow-root}.mw-parser-output .side-box-abovebelow,.mw-parser-output .side-box-text{padding:0.25em 0.9em}.mw-parser-output .side-box-image{padding:2px 0 2px 0.9em;text-align:center}.mw-parser-output .side-box-imageright{padding:2px 0.9em 2px 0;text-align:center}@media(min-width:500px){.mw-parser-output .side-box-flex{display:flex;align-items:center}.mw-parser-output .side-box-text{flex:1}}@media(min-width:720px){.mw-parser-output .side-box{width:238px}.mw-parser-output .side-box-right{clear:right;float:right;margin-left:1em}.mw-parser-output .side-box-left{margin-right:1em}}</style><div class="side-box side-box-right" style="width: 250px;"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r82655520"> <div class="side-box-flex"> <div class="side-box-text plainlist"><a href="/wiki/%E6%9C%AA%E8%A7%A3%E6%B1%BA%E7%9A%84%E7%89%A9%E7%90%86%E5%AD%B8%E5%95%8F%E9%A1%8C" title="未解決的物理學問題">未解決的物理學問題</a>：量子理論的描述怎樣成為做實驗所觀查到的大自然實在，這包括<a href="/wiki/%E6%80%81%E5%8F%A0%E5%8A%A0%E5%8E%9F%E7%90%86" title="态叠加原理">量子態疊加</a>、<a href="/wiki/%E6%B3%A2%E5%87%BD%E6%95%B8%E5%A1%8C%E7%B8%AE" class="mw-redirect" title="波函數塌縮">波函數塌縮</a>、<a href="/wiki/%E9%87%8F%E5%AD%90%E5%8E%BB%E7%9B%B8%E5%B9%B2" class="mw-redirect" title="量子去相干">量子去相干</a>等等？換句話說，這是一種<a href="/wiki/%E9%87%8F%E5%AD%90%E6%B8%AC%E9%87%8F" title="量子測量">測量問題</a>，造成波函數塌縮為<a href="/wiki/%E7%A2%BA%E5%AE%9A%E6%85%8B" class="mw-redirect" title="確定態">確定態</a>的量子測量所倚賴的機制為何？</div> <div class="side-box-imageright"><a href="/wiki/File:Question_mark2.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/b0/Question_mark2.svg/40px-Question_mark2.svg.png" decoding="async" width="40" height="52" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b0/Question_mark2.svg/60px-Question_mark2.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/b0/Question_mark2.svg/80px-Question_mark2.svg.png 2x" data-file-width="71" data-file-height="92" /></a></div></div> </div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r85100532"><div role="note" class="hatnote navigation-not-searchable">主条目：<a href="/wiki/%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%B8%E8%A9%AE%E9%87%8B" title="量子力學詮釋">量子力學詮釋</a></div> 量子力学是經歷最严格验证的物理理论之一。至今为止，尚未找到任何能夠推翻量子力学的实验数据。大多数物理学者认为，“几乎”在所有情况下，它正确地描写能量和物质的物理性质。虽然如此，量子力学中，依然存在着概念上的弱点和缺陷，除前面所述關於万有引力的量子理论的缺乏以外，現今，对於量子力学的<a href="/wiki/%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6%E8%AF%A0%E9%87%8A" class="mw-redirect" title="量子力学诠释">詮释</a>依然存在着嚴重争议。<a href="#cite_note-40">[35]</a><a href="#cite_note-Haroche-35">[30]</a>:4-5 從初始到現今，量子力學的各種反直覺論述與結果一直不停地引起在哲學、詮釋方面的強烈辯論。甚至一些基礎論點，例如，<a href="/wiki/%E9%A6%AC%E5%85%8B%E6%96%AF%C2%B7%E7%8E%BB%E6%81%A9" class="mw-redirect" title="馬克斯·玻恩">馬克斯·玻恩</a>關於概率幅與概率分佈的<a href="/wiki/%E7%8E%BB%E6%81%A9%E5%AE%9A%E5%89%87" title="玻恩定則">基本定則</a>，也需要經過數十年的嚴格思考論證，才被學術界接受。<a href="#cite_note-41">[f]</a><a href="/wiki/%E7%90%86%E5%AF%9F%C2%B7%E8%B2%BB%E6%9B%BC" class="mw-redirect" title="理察·費曼">理察·費曼</a>曾經說過一句銘言：「我認為我可以有把握地說，沒有人懂得量子力學！」<a href="#cite_note-42">[36]</a><a href="/wiki/%E5%8F%B2%E8%92%82%E6%96%87%C2%B7%E6%B8%A9%E4%BC%AF%E6%A0%BC" title="史蒂文·温伯格">史蒂文·溫伯格</a>承認：「依照我現在的看法，完全令人滿意的量子力學詮釋不存在。」<a href="#cite_note-43">[37]</a> 雖然在發表後已經過七十幾年光陰，<a href="/wiki/%E5%93%A5%E6%9C%AC%E5%93%88%E6%A0%B9%E8%A9%AE%E9%87%8B" title="哥本哈根詮釋">哥本哈根詮釋</a>仍舊是最為物理學者接受的對於量子力學的一種詮釋。它的主要貢獻者是<a href="/wiki/%E5%B0%BC%E5%B0%94%E6%96%AF%C2%B7%E7%8E%BB%E5%B0%94" title="尼尔斯·玻尔">尼尔斯·玻尔</a>與<a href="/wiki/%E6%B2%83%E7%BA%B3%C2%B7%E6%B5%B7%E6%A3%AE%E5%A0%A1" class="mw-redirect" title="沃纳·海森堡">沃纳·海森堡</a>。根據這種詮釋，量子力學的概率性論述不是一種暫時補丁，而且最終將會被一種命定性理論取代，它必須被視為一種最終拋棄經典因果論思維的動作。在這裡，任何量子力學形式論的良好定義的應用必須將實驗設置納入考量，這是因為不同實驗狀況獲得的結果所具有的<a href="/wiki/%E4%BA%92%E8%A1%A5%E5%8E%9F%E7%90%86" title="互补原理">互補性</a>。<a href="#cite_note-Laloe-23">[20]</a>:15-16 身為量子理論的創始者之一的愛因斯坦很不滿意這種非命定性的論述。他認為量子力學不具有完備性，他提出一系列反駁論述，其中最著名的就是<a href="/wiki/%E7%88%B1%E5%9B%A0%E6%96%AF%E5%9D%A6-%E6%B3%A2%E5%A4%9A%E5%B0%94%E6%96%AF%E5%9F%BA-%E7%BD%97%E6%A3%AE%E4%BD%AF%E8%B0%AC" title="爱因斯坦-波多尔斯基-罗森佯谬">愛因斯坦-波多爾斯基-羅森佯謬</a>。這佯謬建立於<a href="/wiki/%E7%88%B1%E5%9B%A0%E6%96%AF%E5%9D%A6-%E6%B3%A2%E5%A4%9A%E5%B0%94%E6%96%AF%E5%9F%BA-%E7%BD%97%E6%A3%AE%E4%BD%AF%E8%B0%AC#定域實在論" title="爱因斯坦-波多尔斯基-罗森佯谬">定域實在論</a>。假設局區域實在論成立，則量子力學不具有完備性。接近三十年以後，<a href="/wiki/%E7%B4%84%E7%BF%B0%C2%B7%E8%B2%9D%E7%88%BE" class="mw-disambig" title="約翰·貝爾">約翰·貝爾</a>發佈論文表示，對於這個佯謬稍加理論延伸，就會導致對於量子力學與定域實在論出現不同的預言，因此可以做實驗檢試量子世界到底與哪種預言一致。<a href="#cite_note-Bell1964-44">[38]</a><a href="#cite_note-Aspect1999-45">[39]</a>為此，完成了很多相關實驗，這些實驗確定量子力學的預言正確無誤，定域實在論無法描述量子世界。<a href="#cite_note-46">[40]</a> <a href="/wiki/%E4%BC%91%C2%B7%E8%89%BE%E5%BC%97%E9%9B%B7%E7%89%B9%E4%B8%89%E4%B8%96" title="休·艾弗雷特三世">休·艾弗雷特三世</a>提出的<a href="/wiki/%E5%A4%9A%E4%B8%96%E7%95%8C%E8%AF%A0%E9%87%8A" title="多世界诠释">多世界诠释</a>认为，量子理论所做出的可能性的预言，全部會同步实现，这些现实成为彼此之间毫無關聯的<a href="/wiki/%E5%A4%9A%E4%B8%96%E7%95%8C%E8%AF%A0%E9%87%8A" title="多世界诠释">平行宇宙</a>。在这種诠释裏，波函数不塌缩，它的发展是决定性的。但是由於隻身观察者无法存在於所有的平行宇宙裏，只能观察在身處的宇宙內發生的事件，而無法觀察到其它平行宇宙內發生的事件。这種诠释不需要特殊處理测量動作。在这理论裏，薛定谔方程無論何處無論何時都成立。對於任何測量動作，必須將整個系統，測量儀器與被測量物體，全部納入薛定谔方程的運算。<a href="#cite_note-47">[41]</a><a href="#cite_note-48">[42]</a>測量儀器與被測量物體所有可能的量子態都存在於一種真實的量子疊加，形成了<a href="/wiki/%E9%87%8F%E5%AD%90%E7%BA%A0%E7%BC%A0" class="mw-redirect" title="量子纠缠">糾纏態</a>。雖然平行宇宙具有命定性，觀察者意識到由概率主導的非命定行為，因為觀察者只能觀察到自身所在的宇宙。多世界诠释能夠透過貝爾的檢試實驗。近期研究發展將多世界诠释與<a href="/wiki/%E9%87%8F%E5%AD%90%E9%80%80%E7%9B%B8%E5%B9%B2" title="量子退相干">量子退相干</a>理論合併在一起來解釋主觀的波函數塌縮。由於量子退相干機制，糾纏態會快速地演化為<a href="/wiki/%E5%AF%86%E5%BA%A6%E7%9F%A9%E9%99%A3#混合態" title="密度矩陣">經典混合態</a>。<a href="#cite_note-zeh-49">[43]</a> <a href="/wiki/%E6%88%B4%E7%BB%B4%C2%B7%E7%8E%BB%E5%A7%86" title="戴维·玻姆">戴维·玻姆</a>提出了一種非定域性的<a href="/wiki/%E9%9A%B1%E8%AE%8A%E9%87%8F%E7%90%86%E8%AB%96" title="隱變量理論">隱變量理論</a>，稱為<a href="/wiki/%E5%B0%8E%E8%88%AA%E6%B3%A2%E7%90%86%E8%AB%96" class="mw-redirect" title="導航波理論">導航波理論</a>。在这種詮释裏，波函数被理解为粒子的一个<a href="/wiki/%E5%B0%8E%E8%88%AA%E6%B3%A2%E7%90%86%E8%AB%96" class="mw-redirect" title="導航波理論">導航波</a>。从结果上，这个理论预言的实验结果，与非相对论哥本哈根诠释的预言完全一样，因此，使用实验手段无法鉴别这两个解释。虽然这个理论的预言是命定性的，但是由於不确定原理无法推测出隐变量的精确状态，其结果跟哥本哈根诠释的結果一样，使用導航波理論来解释，实验的结果具有概率性。至今为止，还不能确定这个解释是否能够扩展到相对论量子力学上去。<a href="/wiki/%E8%B7%AF%E6%98%93%C2%B7%E5%BE%B7%E5%B8%83%E7%BD%97%E6%84%8F" title="路易·德布罗意">路易·德布罗意</a>和其他人也提出过类似的隐变量解释。<a href="#cite_note-50">[44]</a><a href="#cite_note-51">[45]</a> <div class="mw-heading mw-heading2"><h2 id="应用">应用</h2>[<a href="/w/index.php?title=%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6&action=edit&section=22" title="编辑章节：应用">编辑</a>]</div> 在许多现代技术装备中，量子效应起了重要的作用，例如，<a href="/wiki/%E6%BF%80%E5%85%89" title="激光">激光</a>的工作機制是<a href="/wiki/%E6%84%9B%E5%9B%A0%E6%96%AF%E5%9D%A6" class="mw-redirect" title="愛因斯坦">愛因斯坦</a>提出的<a href="/wiki/%E5%8F%97%E6%BF%80%E5%8F%91%E5%B0%84" title="受激发射">受激發射</a>、<a href="/wiki/%E9%9B%BB%E5%AD%90%E9%A1%AF%E5%BE%AE%E9%8F%A1" class="mw-redirect" title="電子顯微鏡">电子显微镜</a>利用電子的<a href="/wiki/%E6%B3%A2%E7%B2%92%E4%BA%8C%E8%B1%A1%E6%80%A7" title="波粒二象性">波粒二象性</a>來增加解析度、<a href="/wiki/%E5%8E%9F%E5%AD%90%E9%90%98" title="原子鐘">原子钟</a>使用束縛於原子的<a href="/wiki/%E9%9B%BB%E5%AD%90" class="mw-redirect" title="電子">電子</a>從一個<a href="/wiki/%E8%83%BD%E7%B4%9A" class="mw-redirect" title="能級">能級</a>躍遷至另一個能級時所發射出的<a href="/wiki/%E5%BE%AE%E6%B3%A2" title="微波">微波</a>信號的<a href="/wiki/%E9%A0%BB%E7%8E%87_(%E7%89%A9%E7%90%86%E5%AD%B8)" title="頻率 (物理學)">頻率</a>來計算與維持時間的準確性、<a href="/wiki/%E6%A0%B8%E7%A3%81%E5%85%B1%E6%8C%AF%E6%88%90%E5%83%8F" class="mw-redirect" title="核磁共振成像">核磁共振成像</a>倚賴<a href="/wiki/%E6%A0%B8%E7%A3%81%E5%85%B1%E6%8C%AF" title="核磁共振">核磁共振</a>機制來探測物體內部的結構。对<a href="/wiki/%E5%8D%8A%E5%AF%BC%E4%BD%93" title="半导体">半导体</a>的研究导致了<a href="/wiki/%E4%BA%8C%E6%9E%81%E7%AE%A1" class="mw-redirect" title="二极管">二极管</a>和<a href="/wiki/%E5%8F%8C%E6%9E%81%E6%80%A7%E6%99%B6%E4%BD%93%E7%AE%A1" title="双极性晶体管">三极管</a>的发明，這些都是現代電子系統與電子器件不可或缺的元件。<a href="#cite_note-Haroche-35">[30]</a>:5-10 以下列出了一些量子力學的應用，但實際上其應用不限於這些領域。 <div class="mw-heading mw-heading3"><h3 id="电子器件">电子器件</h3>[<a href="/w/index.php?title=%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6&action=edit&section=23" title="编辑章节：电子器件">编辑</a>]</div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r85100532"><div role="note" class="hatnote navigation-not-searchable">主条目：<a href="/wiki/%E7%94%B5%E5%AD%90%E5%99%A8%E4%BB%B6" class="mw-redirect" title="电子器件">电子器件</a></div> 量子力学在电子器件中得到了广泛应用。比如<a href="/wiki/%E5%8F%91%E5%85%89%E4%BA%8C%E6%9E%81%E7%AE%A1" class="mw-redirect" title="发光二极管">发光二极管</a>在日常照明中应用中越来越广泛<a href="#cite_note-52">[46]</a>。现代计算机的基础，<a href="/wiki/%E5%BE%AE%E5%A4%84%E7%90%86%E5%99%A8" title="微处理器">微处理器</a>，由上亿个半导体<a href="/wiki/%E6%99%B6%E4%BD%93%E7%AE%A1" title="晶体管">晶体管</a>集成，且随着晶体管数量的增加，晶体管中的量子效应越来越明显。量子力学对于解释和模拟半导体器件中的电学、光学、热学性质等尤其重要。<a href="#cite_note-Kragh2002-3">[3]</a>:382-386 量子力学还是量子隧穿器件工作的基础。比如USB非易失性<a href="/wiki/%E9%97%AA%E5%AD%98" title="闪存">闪存</a>中，信息的存储和读取都通过量子隧穿实现。<a href="#cite_note-53">[47]</a> <a href="/wiki/%E8%B6%85%E5%AF%BC" class="mw-redirect" title="超导">超导</a>电子器件也与量子力学有着密切的关系。 <div class="mw-heading mw-heading3"><h3 id="计算机">计算机</h3>[<a href="/w/index.php?title=%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6&action=edit&section=24" title="编辑章节：计算机">编辑</a>]</div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r85100532"><div role="note" class="hatnote navigation-not-searchable">主条目：<a href="/wiki/%E7%94%B5%E5%AD%90%E8%AE%A1%E7%AE%97%E6%9C%BA" title="电子计算机">电子计算机</a>和<a href="/wiki/%E9%87%8F%E5%AD%90%E8%A8%88%E7%AE%97%E6%A9%9F" class="mw-redirect" title="量子計算機">量子計算機</a></div> 相比于晶体管等电子器件，<a href="/wiki/%E9%87%8F%E5%AD%90%E8%AE%A1%E7%AE%97%E6%9C%BA" title="量子计算机">量子计算机</a>的研制则更为前沿。在一些特定算法下，量子计算机的速度会比经典架构的计算机快成千上万倍（比如<a href="/w/index.php?title=%E9%87%8F%E5%AD%90%E9%80%80%E7%81%AB%E7%AE%97%E6%B3%95&action=edit&redlink=1" class="new" title="量子退火算法（页面不存在）">量子退火算法</a>）。经典计算机使用0和1作为<a href="/wiki/%E4%BD%8D%E5%85%83" title="位元">比特</a>，而量子计算机则使用<a href="/wiki/%E9%87%8F%E5%AD%90%E4%BD%8D" class="mw-redirect" title="量子位">量子位</a>作为基本单位。量子位由不同的电子<a href="/wiki/%E6%80%81%E5%8F%A0%E5%8A%A0" class="mw-redirect" title="态叠加">态叠加</a>形成。<a href="#cite_note-Haroche-35">[30]</a>:91-100 <div class="mw-heading mw-heading3"><h3 id="宇宙學">宇宙學</h3>[<a href="/w/index.php?title=%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6&action=edit&section=25" title="编辑章节：宇宙學">编辑</a>]</div> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Cmbr.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/cd/Cmbr.svg/200px-Cmbr.svg.png" decoding="async" width="200" height="160" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/cd/Cmbr.svg/300px-Cmbr.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/cd/Cmbr.svg/400px-Cmbr.svg.png 2x" data-file-width="600" data-file-height="480" /></a><figcaption>由FIRAS儀器對COBE觀測的宇宙微波背景輻射光譜，為最精確測量的<a href="/wiki/%E9%BB%91%E9%AB%94%E8%BC%BB%E5%B0%84" class="mw-redirect" title="黑體輻射">黑體輻射</a>光譜性質，<a href="#cite_note-dpf99-54">[48]</a>即使將圖像放大，誤差範圍也極小，無法由理論曲線中分辨觀測數據。</figcaption></figure> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r85100532"><div role="note" class="hatnote navigation-not-searchable">主条目：<a href="/wiki/%E5%AE%87%E5%AE%99%E5%AD%B8" class="mw-redirect" title="宇宙學">宇宙學</a>和<a href="/wiki/%E9%87%8F%E5%AD%90%E5%AE%87%E5%AE%99%E5%AD%B8" title="量子宇宙學">量子宇宙學</a></div> 量子力學能夠用來解釋很多奇異的宇宙現象，例如，<a href="/wiki/%E5%AE%87%E5%AE%99%E5%BE%AE%E6%B3%A2%E8%83%8C%E6%99%AF" title="宇宙微波背景">宇宙微波背景</a>的<a href="/wiki/%E9%A0%BB%E8%AD%9C" class="mw-redirect" title="頻譜">頻譜</a>可以用<a href="/wiki/%E6%99%AE%E6%9C%97%E5%85%8B%E9%BB%91%E4%BD%93%E8%BE%90%E5%B0%84%E5%AE%9A%E5%BE%8B" title="普朗克黑体辐射定律">普朗克黑體輻射定律</a>來解釋。宇宙微波背景證實了<a href="/wiki/%E5%A4%A7%E7%88%86%E7%82%B8%E7%90%86%E8%AB%96" class="mw-redirect" title="大爆炸理論">大爆炸理論</a>的正確無誤，自此，<a href="/wiki/%E7%A9%A9%E6%85%8B%E7%90%86%E8%AB%96" title="穩態理論">穩態理論</a>開始式微。從宇宙微波背景可以推論，早期宇宙非常炙熱、對於電磁輻射不透明、具有<a href="/wiki/%E5%AE%87%E5%AE%99%E5%AD%B8%E5%8E%9F%E7%90%86" class="mw-redirect" title="宇宙學原理">均質性</a>與<a href="/wiki/%E5%90%84%E5%90%91%E5%90%8C%E6%80%A7" title="各向同性">各向同性</a>，是標準的<a href="/wiki/%E9%BB%91%E4%BD%93_(%E7%89%A9%E7%90%86%E5%AD%A6)" title="黑体 (物理学)">黑體</a>。<a href="#cite_note-Basdevant2007-55">[49]</a>:273<a href="#cite_note-Ryden2003-56">[50]</a>:152 在<a href="/wiki/%E6%81%86%E6%98%9F" class="mw-redirect" title="恆星">恆星</a>的生命終點，當所有核燃料都已用盡，恆星會開始<a href="/wiki/%E5%BC%95%E5%8A%9B%E5%9D%8D%E7%BC%A9" title="引力坍缩">引力坍缩</a>的過程，最終可能變為<a href="/wiki/%E7%99%BD%E7%9F%AE%E6%98%9F" title="白矮星">白矮星</a>、<a href="/wiki/%E4%B8%AD%E5%AD%90%E6%98%9F" title="中子星">中子星</a>或<a href="/wiki/%E9%BB%91%E6%B4%9E" title="黑洞">黑洞</a>。這是因為<a href="/wiki/%E5%8C%85%E7%AB%8B%E4%B8%8D%E7%9B%B8%E5%AE%B9%E5%8E%9F%E7%90%86" class="mw-redirect" title="包立不相容原理">包立不相容原理</a>的作用。由於電子遵守包立不相容原理，因此在坍缩時，假若<a href="/wiki/%E9%9B%BB%E5%AD%90%E7%B0%A1%E4%BD%B5%E5%A3%93%E5%8A%9B" title="電子簡併壓力">電子簡併壓力</a>能夠克服<a href="/wiki/%E5%BC%95%E5%8A%9B" title="引力">引力</a>，就會形成白矮星，否則會繼續坍缩，由於中子也遵守包立不相容原理，這時假若<a href="/wiki/%E7%AE%80%E5%B9%B6%E6%80%81%E7%89%A9%E8%B4%A8" title="简并态物质">中子簡併壓力</a>能夠克服引力，則會形成中子星，否則就會坍缩成黑洞。<a href="#cite_note-Bojowald2012-57">[51]</a>:286-287 <div class="mw-heading mw-heading3"><h3 id="化学">化学</h3>[<a href="/w/index.php?title=%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6&action=edit&section=26" title="编辑章节：化学">编辑</a>]</div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r85100532"><div role="note" class="hatnote navigation-not-searchable">主条目：<a href="/wiki/%E5%8C%96%E5%AD%A6" class="mw-redirect" title="化学">化学</a>和<a href="/wiki/%E9%87%8F%E5%AD%90%E5%8C%96%E5%AD%B8" class="mw-redirect" title="量子化學">量子化學</a></div> 任何物质的化学性質，均是由其原子或分子的电子结构所决定的。通过解析包括了所有相关的原子核和电子的多粒子薛定谔方程，可以计算出该原子或分子的电子结构。在实践中，人们认识到，要计算这样的方程实在太复杂，對於許多案例，必需使用简化的模型，找到可行的數學計算方法，才能夠找到近似的电子结构，從而确定物质的化学性質。<a href="#cite_note-OxtobyGillis2011-58">[52]</a>:193-195實際上，<a href="/wiki/%E9%87%8F%E5%AD%90%E9%9B%BB%E5%8B%95%E5%8A%9B%E5%AD%B8" title="量子電動力學">量子電動力學</a>是化學的基礎原理<a href="#cite_note-FeynmanPhys-59">[53]</a>。 量子力學可以詳細描述原子的電子結構與化學性質。對於只擁有一個束縛電子的<a href="/wiki/%E6%B0%AB%E5%8E%9F%E5%AD%90" title="氫原子">氫原子</a>，<a href="/wiki/%E8%96%9B%E4%B8%81%E6%A0%BC%E6%96%B9%E7%A8%8B%E5%BC%8F" class="mw-redirect" title="薛丁格方程式">薛丁格方程式</a>有<a href="/wiki/%E8%A7%A3%E6%9E%90%E8%A7%A3" title="解析解">解析解</a>，可以計算出相關的<a href="/wiki/%E8%83%BD%E7%B4%9A" class="mw-redirect" title="能級">能級</a>與<a href="/wiki/%E6%B0%AB%E5%8E%9F%E5%AD%90" title="氫原子">氫原子軌域</a>，而且能級符合氫原子光譜實驗的數據，從每一種氫原子軌域可以得到對應的電子概率分佈。對於其它種原子（多電子原子），薛丁格方程式沒有解析解，只能得到近似解，可以計算出近似氫原子軌域的<a href="/wiki/%E5%8E%9F%E5%AD%90%E8%BB%8C%E5%9F%9F" class="mw-redirect" title="原子軌域">哈特里原子軌域</a>，形狀相同，但尺寸與能級模式不一樣。使用哈特里原子軌域，可以解釋原子的電子結構與化學性質，週期表的元素排列。<a href="#cite_note-OxtobyGillis2011-58">[52]</a>:193-195 量子力學能夠解釋，在分子裏的束縛電子怎樣將分子內部的原子綑綁在一起。對於最為簡單，只擁有一個束縛電子的<a href="/wiki/%E6%B0%A2%E5%88%86%E5%AD%90%E7%A6%BB%E5%AD%90" title="氢分子离子">氫分子離子</a>H2+，應用<a href="/wiki/%E7%8E%BB%E6%81%A9%E2%80%93%E5%A5%A5%E6%9C%AC%E6%B5%B7%E9%BB%98%E8%BF%91%E4%BC%BC" class="mw-redirect" title="玻恩–奥本海默近似">玻恩–奥本海默近似</a>（兩個原子核固定不動），<a href="/wiki/%E8%96%9B%E4%B8%81%E6%A0%BC%E6%96%B9%E7%A8%8B%E5%BC%8F" class="mw-redirect" title="薛丁格方程式">薛丁格方程式</a>有解析解，可以計算出它的<a href="/wiki/%E5%88%86%E5%AD%90%E8%BB%8C%E5%9F%9F" class="mw-redirect" title="分子軌域">分子軌域</a>。但是對於其它更為複雜的分子，薛丁格方程式沒有解析解，只能得到近似解，只能計算出近似的分子軌域。<a href="/wiki/%E7%90%86%E8%AE%BA%E5%8C%96%E5%AD%A6" title="理论化学">理论化学</a>中的分支，<a href="/wiki/%E9%87%8F%E5%AD%90%E5%8C%96%E5%AD%A6" title="量子化学">量子化学</a>和<a href="/wiki/%E8%AE%A1%E7%AE%97%E5%8C%96%E5%AD%A6" title="计算化学">计算化学</a>，專注於使用近似的薛定谔方程，来计算复杂的分子的结构及其化学性質。<a href="#cite_note-OxtobyGillis2011-58">[52]</a>:235ff <div class="mw-heading mw-heading3"><h3 id="信息学">信息学</h3>[<a href="/w/index.php?title=%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6&action=edit&section=27" title="编辑章节：信息学">编辑</a>]</div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r85100532"><div role="note" class="hatnote navigation-not-searchable">主条目：<a href="/wiki/%E4%BF%A1%E6%81%AF%E5%AD%B8" class="mw-redirect" title="信息學">信息學</a>和<a href="/wiki/%E9%87%8F%E5%AD%90%E4%BF%A1%E6%81%AF%E5%AD%B8" class="mw-redirect" title="量子信息學">量子信息學</a></div> 目前的研究聚焦於找到可靠與能夠直接处理量子态的方法。量子系統擁有一種特性，即對於量子數據的測量會不可避免地改變數據，這種特性可以用來偵測出任何竊聽動作。倚賴這特性，<a href="/wiki/%E9%87%8F%E5%AD%90%E5%AF%86%E7%A2%BC%E5%AD%B8" title="量子密碼學">量子密碼學</a>能夠保證<a href="/wiki/%E9%80%9A%E4%BF%A1" title="通信">通信</a>安全性，使得通信双方能够产生并分享一个随机的，安全的<a href="/wiki/%E5%AF%86%E9%92%A5" title="密钥">密钥</a>，来加密和解密信息。比較遙遠的目標是發展出量子電腦。由於量子态具有量子叠加的特性，理论而言，量子電腦可以達成高度<a href="/wiki/%E5%B9%B6%E8%A1%8C%E8%AE%A1%E7%AE%97" title="并行计算">并行计算</a>，其計算速度有可能以指數函數快過普通電腦。另外，應用量子纏結特性與經典通訊理論，<a href="/wiki/%E9%87%8F%E5%AD%90%E9%81%99%E5%82%B3" class="mw-redirect" title="量子遙傳">量子遙傳</a>能夠將物體的量子態從某個位置傳送至另一個位置。這是正在積極進行的一門學術領域。<a href="#cite_note-NielsenChuang2010-60">[54]</a> <div class="mw-heading mw-heading2"><h2 id="参见">参见</h2>[<a href="/w/index.php?title=%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6&action=edit&section=28" title="编辑章节：参见">编辑</a>]</div> <div role="navigation" aria-label="Portals" class="noprint portal plainlist tright" style="margin:0.5em 0 0.5em 1em;border:solid #aaa 1px"> <ul style="display:table;box-sizing:border-box;padding:0.1em;max-width:175px;background:var(--background-color-base,#f9f9f9);font-size:85%;line-height:110%;font-weight:bold"> <li style="display:table-row"><a href="/wiki/File:Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg" class="mw-file-description"><img alt="icon" src="//upload.wikimedia.org/wikipedia/commons/thumb/6/6f/Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg/25px-Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg.png" decoding="async" width="25" height="28" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/6f/Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg/37px-Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/6f/Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg/49px-Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg.png 2x" data-file-width="530" data-file-height="600" /></a><a href="/wiki/Portal:%E7%89%A9%E7%90%86%E5%AD%A6" title="Portal:物理学">物理学主题</a></li></ul></div> <style data-mw-deduplicate="TemplateStyles:r79074265">.mw-parser-output .div-col{margin-top:0.3em;column-width:30em}.mw-parser-output .div-col-small{font-size:90%}.mw-parser-output .div-col-rules{column-rule:1px solid #aaa}.mw-parser-output .div-col dl,.mw-parser-output .div-col ol,.mw-parser-output .div-col ul{margin-top:0}.mw-parser-output .div-col li,.mw-parser-output .div-col dd{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .plainlist ol,.mw-parser-output .plainlist ul{line-height:inherit;list-style:none;margin:0}.mw-parser-output .plainlist ol li,.mw-parser-output .plainlist ul li{margin-bottom:0}</style><div class="div-col" style="column-width:35em;"> <ul><li><a href="/wiki/%E7%8B%84%E6%8B%89%E5%85%8B%E7%AC%A6%E5%8F%B7" title="狄拉克符号">狄拉克符号</a></li> <li><a href="/wiki/%E6%99%AE%E6%9C%97%E5%85%8B%E5%96%AE%E4%BD%8D%E5%88%B6" title="普朗克單位制">普朗克單位制</a></li> <li><a href="/wiki/%E7%9B%B8%E7%A9%BA%E9%97%B4%E8%A1%A8%E8%BF%B0" title="相空间表述">相空间表述</a></li> <li><a href="/wiki/%E6%AD%A3%E8%A6%8F%E5%8C%96" title="正規化">正規化</a></li> <li><a href="/wiki/%E9%9B%99%E6%85%8B%E7%B3%BB%E7%B5%B1" title="雙態系統">雙態系統</a></li></ul> </div> <div class="mw-heading mw-heading2"><h2 id="註釋">註釋</h2>[<a href="/w/index.php?title=%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6&action=edit&section=29" title="编辑章节：註釋">编辑</a>]</div> <div class="notelist" style="list-style-type: lower-alpha;"> <ol class="references"> <li id="cite_note-4"><a href="#cite_ref-4">^</a> 1922年，<a href="/wiki/%E9%98%BF%E5%B0%94%E4%BC%AF%E7%89%B9%C2%B7%E7%88%B1%E5%9B%A0%E6%96%AF%E5%9D%A6" title="阿尔伯特·爱因斯坦">阿尔伯特·爱因斯坦</a>评价当时对于<a href="/wiki/%E8%B6%85%E5%AF%BC" class="mw-redirect" title="超导">超导</a>的理论解释：“目前我们对于复合系统的量子力学的深远意义仍一无所知。在这些模糊的概念的基础上，我们距离构造出（能描述超导现象的）理论的目标仍很遥远。<a href="#cite_note-Kragh2002-3">[3]</a>:86 </li> <li id="cite_note-ElectronDetection-12">^ <a href="#cite_ref-ElectronDetection_12-0">2.0</a> <a href="#cite_ref-ElectronDetection_12-1">2.1</a> 雖然每一點表示一個電子抵達探測屏，這事實無法表現出電子的粒子性，因為探測器是由離散原子組成的，這可以詮釋為電子波與離散原子彼此之間的相互作用。<a href="#cite_note-Hobson-11">[10]</a> </li> <li id="cite_note-20"><a href="#cite_ref-20">^</a> 使用可觀察量 <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7daff47fa58cdfd29dc333def748ff5fa4c923e3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle A}">的基底<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle e_{1},e_{2},\dots ,e_{n}\ }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>,</mo> <mo>…</mo> <mo>,</mo> <msub> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> <mtext> </mtext> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle e_{1},e_{2},\dots ,e_{n}\ }</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/78bb4d5ec31ee5b825d1373d937459bde6ddaefe" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:13.37ex; height:2.009ex;" alt="{\displaystyle e_{1},e_{2},\dots ,e_{n}\ }">，量子態 <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle |\psi \rangle }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>ψ</mi> <mo fence="false" stretchy="false">⟩</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle |\psi \rangle }</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cc27f1893b769a08cd6b296e115a29e61cab675e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:3.065ex; height:2.843ex;" alt="{\displaystyle |\psi \rangle }">可以表示為<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle |\psi \rangle =\sum _{j}c_{j}|e_{j}\rangle }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>ψ</mi> <mo fence="false" stretchy="false">⟩</mo> <mo>=</mo> <munder> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </munder> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <msub> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> <mo fence="false" stretchy="false">⟩</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle |\psi \rangle =\sum _{j}c_{j}|e_{j}\rangle }</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bab88f6f60f6d90fce1ab0876f8d8751edef0fae" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.338ex; width:15.366ex; height:5.843ex;" alt="{\displaystyle |\psi \rangle =\sum _{j}c_{j}|e_{j}\rangle }">；其中<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle c_{j}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle c_{j}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a844d180d176af828d1636d4e85aa534d0b77baa" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:1.917ex; height:2.343ex;" alt="{\displaystyle c_{j}}">是量子態<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle |\psi \rangle }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>ψ</mi> <mo fence="false" stretchy="false">⟩</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle |\psi \rangle }</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cc27f1893b769a08cd6b296e115a29e61cab675e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:3.065ex; height:2.843ex;" alt="{\displaystyle |\psi \rangle }">處於本徵態<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle |e_{j}\rangle }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <msub> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> <mo fence="false" stretchy="false">⟩</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle |e_{j}\rangle }</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8860efe6010c3229d844219d56780c7ed08a7acf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:3.545ex; height:3.009ex;" alt="{\displaystyle |e_{j}\rangle }">的<a href="/w/index.php?title=%E6%A6%82%E7%8E%87%E5%B9%85&action=edit&redlink=1" class="new" title="概率幅（页面不存在）">概率幅</a>。根據<a href="/wiki/%E6%B3%A2%E6%81%A9%E5%AE%9A%E5%89%87" class="mw-redirect" title="波恩定則">波恩定則</a>，對於這測量，獲得本徵值 <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a_{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a_{i}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0bc77764b2e74e64a63341054fa90f3e07db275f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.029ex; height:2.009ex;" alt="{\displaystyle a_{i}}"> 的概率為 <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle |\langle e_{i}|\psi \rangle |^{2}=|c_{i}|^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mo fence="false" stretchy="false">⟨</mo> <msub> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>ψ</mi> <mo fence="false" stretchy="false">⟩</mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <msup> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle |\langle e_{i}|\psi \rangle |^{2}=|c_{i}|^{2}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7ec95f0160bbb526dfd579dfd27f60df3fe04745" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:15.453ex; height:3.343ex;" alt="{\displaystyle |\langle e_{i}|\psi \rangle |^{2}=|c_{i}|^{2}}">。 </li> <li id="cite_note-27"><a href="#cite_ref-27">^</a> 反對稱性波函數為 <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle [\sin(x)\sin(3y)-\sin(3x)\sin(y)]/{\sqrt {2}},\qquad 0\leq x,y\leq \pi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">[</mo> <mi>sin</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mi>sin</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mn>3</mn> <mi>y</mi> <mo stretchy="false">)</mo> <mo>−</mo> <mi>sin</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mn>3</mn> <mi>x</mi> <mo stretchy="false">)</mo> <mi>sin</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>y</mi> <mo stretchy="false">)</mo> <mo stretchy="false">]</mo> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>2</mn> </msqrt> </mrow> <mo>,</mo> <mspace width="2em" /> <mn>0</mn> <mo>≤</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>≤</mo> <mi>π</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle [\sin(x)\sin(3y)-\sin(3x)\sin(y)]/{\sqrt {2}},\qquad 0\leq x,y\leq \pi }</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6a7e33ba5223d7e206aaa549461838525f8a7112" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:53.014ex; height:3.176ex;" alt="{\displaystyle [\sin(x)\sin(3y)-\sin(3x)\sin(y)]/{\sqrt {2}},\qquad 0\leq x,y\leq \pi }"> 。注意到在 <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x=y}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> <mo>=</mo> <mi>y</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x=y}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/409a91214d63eabe46ec10ff3cbba689ab687366" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:5.584ex; height:2.009ex;" alt="{\displaystyle x=y}"> 附近，概率幅絕對值很微小，兩個費米子趨向於彼此互相遠離對方。 </li> <li id="cite_note-28"><a href="#cite_ref-28">^</a> 對稱性波函數為 <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle -[\sin(x)\sin(3y)+\sin(3x)\sin(y)]/{\sqrt {2}},\qquad 0\leq x,y\leq \pi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>−</mo> <mo stretchy="false">[</mo> <mi>sin</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mi>sin</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mn>3</mn> <mi>y</mi> <mo stretchy="false">)</mo> <mo>+</mo> <mi>sin</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mn>3</mn> <mi>x</mi> <mo stretchy="false">)</mo> <mi>sin</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>y</mi> <mo stretchy="false">)</mo> <mo stretchy="false">]</mo> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>2</mn> </msqrt> </mrow> <mo>,</mo> <mspace width="2em" /> <mn>0</mn> <mo>≤</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>≤</mo> <mi>π</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle -[\sin(x)\sin(3y)+\sin(3x)\sin(y)]/{\sqrt {2}},\qquad 0\leq x,y\leq \pi }</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7235bd6d0756b86e8d42fd9d915180aa257db20a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:54.822ex; height:3.176ex;" alt="{\displaystyle -[\sin(x)\sin(3y)+\sin(3x)\sin(y)]/{\sqrt {2}},\qquad 0\leq x,y\leq \pi }"> 。注意到在 <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x=y}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> <mo>=</mo> <mi>y</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x=y}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/409a91214d63eabe46ec10ff3cbba689ab687366" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:5.584ex; height:2.009ex;" alt="{\displaystyle x=y}"> 附近，概率幅絕對值較大，兩個玻色子趨向於彼此互相接近對方。 </li> <li id="cite_note-41"><a href="#cite_ref-41">^</a> 玻恩詮釋波函數為在某時間、某位置找到粒子的概率幅。這是一種粒子論。波函數也可以詮釋為「在某時間、某位置發生相互作用的概率輻」。這較寬鬆的詮釋方式可以適用於波動論或粒子論。<a href="#cite_note-Hobson-11">[10]</a> </li> </ol> </div> <div class="mw-heading mw-heading2"><h2 id="参考文献">参考文献</h2>[<a href="/w/index.php?title=%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6&action=edit&section=30" title="编辑章节：参考文献">编辑</a>]</div> <div class="reflist references-column-width" style="-moz-column-width: 30em; -webkit-column-width: 30em; column-width: 30em; list-style-type: decimal;"> <ol class="references"> <li id="cite_note-Born1926-1"><a href="#cite_ref-Born1926_1-0">^</a> <cite class="citation journal"><a href="/wiki/Max_Born" class="mw-redirect" title="Max Born">Born, M.</a> Zur Quantenmechanik der Stoßvorgänge [On the Quantum Mechanics of Collision Processes]. Zeitschrift für Physik. 1926, 37 (12): 863–867. <a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1926ZPhy...37..863B">Bibcode:1926ZPhy...37..863B</a>. <a rel="nofollow" class="external text" href="//www.worldcat.org/issn/1434-6001">ISSN 1434-6001</a>. <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:119896026">S2CID 119896026</a>. <a rel="nofollow" class="external text" href="https://doi.org/10.1007%2FBF01397477">doi:10.1007/BF01397477</a>.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6&rft.atitle=Zur+Quantenmechanik+der+Sto%C3%9Fvorg%C3%A4nge&rft.aufirst=M.&rft.aulast=Born&rft.date=1926&rft.genre=article&rft.issn=1434-6001&rft.issue=12&rft.jtitle=Zeitschrift+f%C3%BCr+Physik&rft.pages=863-867&rft.volume=37&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A119896026&rft_id=info%3Abibcode%2F1926ZPhy...37..863B&rft_id=info%3Adoi%2F10.1007%2FBF01397477&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal" class="Z3988">  </li> <li id="cite_note-Feynman-2"><a href="#cite_ref-Feynman_2-0">^</a> <cite class="citation book">Feynman, Richard; Leighton, Robert; Sands, Matthew. <a rel="nofollow" class="external text" href="https://feynmanlectures.caltech.edu/III_01.html">The Feynman Lectures on Physics</a> 3. California Institute of Technology. 1964 [19 December 2020]. <a href="/wiki/Special:%E7%BD%91%E7%BB%9C%E4%B9%A6%E6%BA%90/978-0201500646" title="Special:网络书源/978-0201500646">ISBN 978-0201500646</a>. （原始内容<a rel="nofollow" class="external text" href="https://web.archive.org/web/20230607190329/https://www.feynmanlectures.caltech.edu/III_01.html">存档</a>于2023-06-07）.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6&rft.au=Leighton%2C+Robert&rft.au=Sands%2C+Matthew&rft.aufirst=Richard&rft.aulast=Feynman&rft.btitle=The+Feynman+Lectures+on+Physics&rft.date=1964&rft.genre=book&rft.isbn=978-0201500646&rft.pub=California+Institute+of+Technology&rft_id=https%3A%2F%2Ffeynmanlectures.caltech.edu%2FIII_01.html&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988">  </li> <li id="cite_note-Kragh2002-3">^ <a href="#cite_ref-Kragh2002_3-0">3.0</a> <a href="#cite_ref-Kragh2002_3-1">3.1</a> <a href="#cite_ref-Kragh2002_3-2">3.2</a> <a href="#cite_ref-Kragh2002_3-3">3.3</a> <a href="#cite_ref-Kragh2002_3-4">3.4</a> <a href="#cite_ref-Kragh2002_3-5">3.5</a> <a href="#cite_ref-Kragh2002_3-6">3.6</a> <a href="#cite_ref-Kragh2002_3-7">3.7</a> <a href="#cite_ref-Kragh2002_3-8">3.8</a> <cite class="citation book">Kragh, Helge. Quantum Generations: A History of Physics in the Twentieth Century Reprint. Princeton University Press. 2002. <a href="/wiki/Special:%E7%BD%91%E7%BB%9C%E4%B9%A6%E6%BA%90/978-0691095523" title="Special:网络书源/978-0691095523">ISBN 978-0691095523</a>.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6&rft.aufirst=Helge&rft.aulast=Kragh&rft.btitle=Quantum+Generations%3A+A+History+of+Physics+in+the+Twentieth+Century&rft.date=2002&rft.edition=Reprint&rft.genre=book&rft.isbn=978-0691095523&rft.pub=Princeton+University+Press&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988">  </li> <li id="cite_note-5"><a href="#cite_ref-5">^</a> 参见中文简体SI版《伯克利物理学教程》第四卷第24页，1.38小节 </li> <li id="cite_note-Heisenberg1999-6"><a href="#cite_ref-Heisenberg1999_6-0">^</a> <cite class="citation book">Werner Heisenberg. <a rel="nofollow" class="external text" href="https://archive.org/details/PhysicsPhilosophy">Physics and Philosophy: The Revolution in Modern Science</a>. Prometheus Books. 1999. <a href="/wiki/Special:%E7%BD%91%E7%BB%9C%E4%B9%A6%E6%BA%90/978-1-57392-694-2" title="Special:网络书源/978-1-57392-694-2">ISBN 978-1-57392-694-2</a>.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6&rft.au=Werner+Heisenberg&rft.btitle=Physics+and+Philosophy%3A+The+Revolution+in+Modern+Science&rft.date=1999&rft.genre=book&rft.isbn=978-1-57392-694-2&rft.pub=Prometheus+Books&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2FPhysicsPhilosophy&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988">  </li> <li id="cite_note-Pais1982-7"><a href="#cite_ref-Pais1982_7-0">^</a> <cite class="citation book">Abraham Pais. Subtle is the Lord : The Science and the Life of Albert Einstein: The Science and the Life of Albert Einstein. Oxford University Press. 23 September 1982. <a href="/wiki/Special:%E7%BD%91%E7%BB%9C%E4%B9%A6%E6%BA%90/978-0-19-152402-8" title="Special:网络书源/978-0-19-152402-8">ISBN 978-0-19-152402-8</a>.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6&rft.au=Abraham+Pais&rft.btitle=Subtle+is+the+Lord+%3A+The+Science+and+the+Life+of+Albert+Einstein%3A+The+Science+and+the+Life+of+Albert+Einstein&rft.date=1982-09-23&rft.genre=book&rft.isbn=978-0-19-152402-8&rft.pub=Oxford+University+Press&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988">  </li> <li id="cite_note-Halliday-8">^ <a href="#cite_ref-Halliday_8-0">7.0</a> <a href="#cite_ref-Halliday_8-1">7.1</a> <cite id="CITEREFHallidayResnickWalker2005" class="citation">Halliday, David; Resnick, Robert; Walker, Jerl, Fundamental of Physics 7th, USA: John Wiley and Sons, Inc., 2005, <a href="/wiki/Special:%E7%BD%91%E7%BB%9C%E4%B9%A6%E6%BA%90/0-471-23231-9" title="Special:网络书源/0-471-23231-9">ISBN 0-471-23231-9</a></cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6&rft.au=Resnick%2C+Robert&rft.au=Walker%2C+Jerl&rft.aufirst=David&rft.aulast=Halliday&rft.btitle=Fundamental+of+Physics&rft.date=2005&rft.edition=7th&rft.genre=book&rft.isbn=0-471-23231-9&rft.place=USA&rft.pub=John+Wiley+and+Sons%2C+Inc.&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988">  </li> <li id="cite_note-Akhlesh_Lakhtakia_Ed._1996-9"><a href="#cite_ref-Akhlesh_Lakhtakia_Ed._1996_9-0">^</a> <cite class="citation journal">Akhlesh Lakhtakia (Ed.); Salpeter, Edwin E. Models and Modelers of Hydrogen. American Journal of Physics (World Scientific). 1996, 65 (9): 933. <a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1997AmJPh..65..933L">Bibcode:1997AmJPh..65..933L</a>. <a href="/wiki/Special:%E7%BD%91%E7%BB%9C%E4%B9%A6%E6%BA%90/981-02-2302-1" title="Special:网络书源/981-02-2302-1">ISBN 981-02-2302-1</a>. <a rel="nofollow" class="external text" href="https://doi.org/10.1119%2F1.18691">doi:10.1119/1.18691</a>.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6&rft.atitle=Models+and+Modelers+of+Hydrogen&rft.au=Akhlesh+Lakhtakia+%28Ed.%29&rft.au=Salpeter%2C+Edwin+E.&rft.date=1996&rft.genre=article&rft.isbn=981-02-2302-1&rft.issue=9&rft.jtitle=American+Journal+of+Physics&rft.pages=933&rft.volume=65&rft_id=info%3Abibcode%2F1997AmJPh..65..933L&rft_id=info%3Adoi%2F10.1119%2F1.18691&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal" class="Z3988">  </li> <li id="cite_note-French1978-10">^ <a href="#cite_ref-French1978_10-0">9.0</a> <a href="#cite_ref-French1978_10-1">9.1</a> <cite id="CITEREFFrench1978" class="citation">French, Anthony, An Introduction to Quantum Physics, W. W. Norton, Inc., 1978</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6&rft.aufirst=Anthony&rft.aulast=French&rft.btitle=An+Introduction+to+Quantum+Physics&rft.date=1978&rft.genre=book&rft.pub=W.+W.+Norton%2C+Inc.&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988">  </li> <li id="cite_note-Hobson-11">^ <a href="#cite_ref-Hobson_11-0">10.0</a> <a href="#cite_ref-Hobson_11-1">10.1</a> <a href="#cite_ref-Hobson_11-2">10.2</a> <cite class="citation journal">Hobson, Art. <a rel="nofollow" class="external text" href="http://arxiv.org/abs/1204.4616">There are no particles, there are only fields</a>. American Journal of Physics. 2013, 81 (211) [2014-09-25]. <a rel="nofollow" class="external text" href="https://doi.org/10.1119%2F1.4789885">doi:10.1119/1.4789885</a>. （原始内容<a rel="nofollow" class="external text" href="https://web.archive.org/web/20150210063318/http://arxiv.org/abs/1204.4616">存档</a>于2015-02-10）.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6&rft.atitle=There+are+no+particles%2C+there+are+only+fields&rft.aufirst=Art&rft.aulast=Hobson&rft.date=2013&rft.genre=article&rft.issue=211&rft.jtitle=American+Journal+of+Physics&rft.volume=81&rft_id=http%3A%2F%2Farxiv.org%2Fabs%2F1204.4616&rft_id=info%3Adoi%2F10.1119%2F1.4789885&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal" class="Z3988">  </li> <li id="cite_note-Tonomura1988-13">^ <a href="#cite_ref-Tonomura1988_13-0">11.0</a> <a href="#cite_ref-Tonomura1988_13-1">11.1</a> <cite class="citation journal">Tonomura, Akira; et al. Demonstration of single‐electron buildup of an interference pattern. American Journal of Physics. 1988, 57 (2): 117–120. <a rel="nofollow" class="external text" href="https://doi.org/10.1119%2F1.16104">doi:10.1119/1.16104</a>.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6&rft.atitle=Demonstration+of+single%E2%80%90electron+buildup+of+an+interference+pattern&rft.aufirst=Akira&rft.aulast=Tonomura&rft.date=1988&rft.genre=article&rft.issue=2&rft.jtitle=American+Journal+of+Physics&rft.pages=117-120&rft.volume=57&rft_id=info%3Adoi%2F10.1119%2F1.16104&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal" class="Z3988">  引文使用过时参数<code style="color:inherit; border:inherit; padding:inherit;">coauthors</code> (<a href="/wiki/Help:%E5%BC%95%E6%96%87%E6%A0%BC%E5%BC%8F1%E9%94%99%E8%AF%AF#deprecated_params" title="Help:引文格式1错误">帮助</a>) </li> <li id="cite_note-14"><a href="#cite_ref-14">^</a> <cite class="citation book">Davisson, Clinton. The Discovery of Electron Waves. <a rel="nofollow" class="external text" href="http://nobelprize.org/nobel_prizes/physics/laureates/1937/davisson-lecture.html">Nobel Lectures, Physics 1922-1941</a>. Amsterdam: Elsevier Publishing Company. 1965 [2007-09-17]. （原始内容<a rel="nofollow" class="external text" href="https://web.archive.org/web/20170827084747/http://nobelprize.org/nobel_prizes/physics/laureates/1937/davisson-lecture.html">存档</a>于2017-08-27）.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6&rft.atitle=The+Discovery+of+Electron+Waves&rft.aufirst=Clinton&rft.aulast=Davisson&rft.btitle=Nobel+Lectures%2C+Physics+1922-1941&rft.date=1965&rft.genre=bookitem&rft.place=Amsterdam&rft.pub=Elsevier+Publishing+Company&rft_id=http%3A%2F%2Fnobelprize.org%2Fnobel_prizes%2Fphysics%2Flaureates%2F1937%2Fdavisson-lecture.html&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988">  </li> <li id="cite_note-Feynman_2006-15"><a href="#cite_ref-Feynman_2006_15-0">^</a> <cite class="citation book">費曼, 理查; 雷頓, 羅伯; 山德士, 馬修. 費曼物理學講義 III (1) 量子行為. 台灣: 天下文化書. 2006: pp. 38–60. <a href="/wiki/Special:%E7%BD%91%E7%BB%9C%E4%B9%A6%E6%BA%90/986-417-672-2" title="Special:网络书源/986-417-672-2">ISBN 986-417-672-2</a>.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6&rft.au=%E5%B1%B1%E5%BE%B7%E5%A3%AB%2C+%E9%A6%AC%E4%BF%AE&rft.au=%E9%9B%B7%E9%A0%93%2C+%E7%BE%85%E4%BC%AF&rft.aufirst=%E7%90%86%E6%9F%A5&rft.aulast=%E8%B2%BB%E6%9B%BC&rft.btitle=%E8%B2%BB%E6%9B%BC%E7%89%A9%E7%90%86%E5%AD%B8%E8%AC%9B%E7%BE%A9+III+%281%29+%E9%87%8F%E5%AD%90%E8%A1%8C%E7%82%BA&rft.date=2006&rft.genre=book&rft.isbn=986-417-672-2&rft.pages=pp.+38-60&rft.place=%E5%8F%B0%E7%81%A3&rft.pub=%E5%A4%A9%E4%B8%8B%E6%96%87%E5%8C%96%E6%9B%B8&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988">  引文格式1维护：冗余文本 (<a href="/wiki/Category:%E5%BC%95%E6%96%87%E6%A0%BC%E5%BC%8F1%E7%BB%B4%E6%8A%A4%EF%BC%9A%E5%86%97%E4%BD%99%E6%96%87%E6%9C%AC" title="Category:引文格式1维护：冗余文本">link</a>) </li> <li id="cite_note-Neumann1932-16"><a href="#cite_ref-Neumann1932_16-0">^</a> <cite class="citation book">von Neumann, John. Mathematical Foundations of Quantum Mechanics 1996. Princeton Univ. Press. 1932. <a href="/wiki/Special:%E7%BD%91%E7%BB%9C%E4%B9%A6%E6%BA%90/0-691-02893-1" title="Special:网络书源/0-691-02893-1">ISBN 0-691-02893-1</a>.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6&rft.aufirst=John&rft.aulast=von+Neumann&rft.btitle=Mathematical+Foundations+of+Quantum+Mechanics&rft.date=1932&rft.edition=1996&rft.genre=book&rft.isbn=0-691-02893-1&rft.pub=Princeton+Univ.+Press&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988">  </li> <li id="cite_note-17"><a href="#cite_ref-17">^</a> <cite class="citation journal">Zurek, Wojciech. <a rel="nofollow" class="external text" href="https://archive.org/details/sim_physics-today_2014-10_67_10/page/44">Quantum Darwinism, Classical Reality, and the randomness of quantum jumps</a>. Physics Today. 2014, 67 (10): 44–45.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6&rft.atitle=Quantum+Darwinism%2C+Classical+Reality%2C+and+the+randomness+of+quantum+jumps&rft.aufirst=Wojciech&rft.aulast=Zurek&rft.date=2014&rft.genre=article&rft.issue=10&rft.jtitle=Physics+Today&rft.pages=44-45&rft.volume=67&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fsim_physics-today_2014-10_67_10%2Fpage%2F44&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal" class="Z3988">  </li> <li id="cite_note-Laloë-18"><a href="#cite_ref-Laloë_18-0">^</a> <cite class="citation book">Claude Cohen-Tannoudji, Bernard Diu, Franck Laloë. Quantum Mechanics Volume 1. Hermann. <a href="/wiki/Special:%E7%BD%91%E7%BB%9C%E4%B9%A6%E6%BA%90/978-2-7056-8392-4" title="Special:网络书源/978-2-7056-8392-4">ISBN 978-2-7056-8392-4</a>.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6&rft.au=Claude+Cohen-Tannoudji%2C+Bernard+Diu%2C+Franck+Lalo%C3%AB&rft.btitle=Quantum+Mechanics+Volume+1&rft.genre=book&rft.isbn=978-2-7056-8392-4&rft.pub=Hermann&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988">  </li> <li id="cite_note-Zettili2009-19"><a href="#cite_ref-Zettili2009_19-0">^</a> <cite class="citation book">Nouredine Zettili. Quantum Mechanics: Concepts and Applications. John Wiley & Sons. 17 February 2009. <a href="/wiki/Special:%E7%BD%91%E7%BB%9C%E4%B9%A6%E6%BA%90/978-0-470-02678-6" title="Special:网络书源/978-0-470-02678-6">ISBN 978-0-470-02678-6</a>.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6&rft.au=Nouredine+Zettili&rft.btitle=Quantum+Mechanics%3A+Concepts+and+Applications&rft.date=2009-02-17&rft.genre=book&rft.isbn=978-0-470-02678-6&rft.pub=John+Wiley+%26+Sons&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988">  使用<code style="color:inherit; border:inherit; padding:inherit;">|accessdate=</code>需要含有<code style="color:inherit; border:inherit; padding:inherit;">|url=</code> (<a href="/wiki/Help:%E5%BC%95%E6%96%87%E6%A0%BC%E5%BC%8F1%E9%94%99%E8%AF%AF#accessdate_missing_url" title="Help:引文格式1错误">帮助</a>) </li> <li id="cite_note-Sakurai-21">^ <a href="#cite_ref-Sakurai_21-0">18.0</a> <a href="#cite_ref-Sakurai_21-1">18.1</a> <a href="#cite_ref-Sakurai_21-2">18.2</a> <a href="#cite_ref-Sakurai_21-3">18.3</a> <a href="#cite_ref-Sakurai_21-4">18.4</a> <a href="#cite_ref-Sakurai_21-5">18.5</a> <a href="#cite_ref-Sakurai_21-6">18.6</a> <a href="#cite_ref-Sakurai_21-7">18.7</a> <cite id="CITEREFSakuraiNapolitano2010" class="citation">Sakurai, J. J.; Napolitano, Jim, Modern Quantum Mechanics 2nd, Addison-Wesley, 2010, <a href="/wiki/Special:%E7%BD%91%E7%BB%9C%E4%B9%A6%E6%BA%90/978-0805382914" title="Special:网络书源/978-0805382914">ISBN 978-0805382914</a></cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6&rft.au=Napolitano%2C+Jim&rft.aufirst=J.+J.&rft.aulast=Sakurai&rft.btitle=Modern+Quantum+Mechanics&rft.date=2010&rft.edition=2nd&rft.genre=book&rft.isbn=978-0805382914&rft.pub=Addison-Wesley&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988">  </li> <li id="cite_note-Griffiths2004-22">^ <a href="#cite_ref-Griffiths2004_22-0">19.0</a> <a href="#cite_ref-Griffiths2004_22-1">19.1</a> <a href="#cite_ref-Griffiths2004_22-2">19.2</a> <a href="#cite_ref-Griffiths2004_22-3">19.3</a> <a href="#cite_ref-Griffiths2004_22-4">19.4</a> <a href="#cite_ref-Griffiths2004_22-5">19.5</a> <a href="#cite_ref-Griffiths2004_22-6">19.6</a> <a href="#cite_ref-Griffiths2004_22-7">19.7</a> <a href="#cite_ref-Griffiths2004_22-8">19.8</a> <cite id="CITEREFGriffiths,_David_J.2004" class="citation">Griffiths, David J., Introduction to Quantum Mechanics (2nd ed.), Prentice Hall, 2004, <a href="/wiki/Special:%E7%BD%91%E7%BB%9C%E4%B9%A6%E6%BA%90/0-13-111892-7" title="Special:网络书源/0-13-111892-7">ISBN 0-13-111892-7</a></cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6&rft.au=Griffiths%2C+David+J.&rft.btitle=Introduction+to+Quantum+Mechanics+%282nd+ed.%29&rft.date=2004&rft.genre=book&rft.isbn=0-13-111892-7&rft.pub=Prentice+Hall&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988">  </li> <li id="cite_note-Laloe-23">^ <a href="#cite_ref-Laloe_23-0">20.0</a> <a href="#cite_ref-Laloe_23-1">20.1</a> <a href="#cite_ref-Laloe_23-2">20.2</a> <a href="#cite_ref-Laloe_23-3">20.3</a> <a href="#cite_ref-Laloe_23-4">20.4</a> <cite id="CITEREFLaloe2012" class="citation">Laloe, Franck, Do We Really Understand Quantum Mechanics, Cambridge University Press, 2012, <a href="/wiki/Special:%E7%BD%91%E7%BB%9C%E4%B9%A6%E6%BA%90/978-1-107-02501-1" title="Special:网络书源/978-1-107-02501-1">ISBN 978-1-107-02501-1</a></cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6&rft.aufirst=Franck&rft.aulast=Laloe&rft.btitle=Do+We+Really+Understand+Quantum+Mechanics&rft.date=2012&rft.genre=book&rft.isbn=978-1-107-02501-1&rft.pub=Cambridge+University+Press&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988">  </li> <li id="cite_note-SEP_measurement-24"><a href="#cite_ref-SEP_measurement_24-0">^</a> <cite class="citation web">Krips, Henry. <a rel="nofollow" class="external text" href="http://plato.stanford.edu/entries/qt-measurement/">Measurement in Quantum Theory</a>. Stanford Encyclopedia of Philosophy. Aug 22, 2007 [2006-10-05]. （原始内容<a rel="nofollow" class="external text" href="https://web.archive.org/web/20210508111958/https://plato.stanford.edu/entries/qt-measurement/">存档</a>于2021-05-08）.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6&rft.atitle=Measurement+in+Quantum+Theory&rft.aufirst=Henry&rft.aulast=Krips&rft.date=2007-08-22&rft.genre=unknown&rft.jtitle=Stanford+Encyclopedia+of+Philosophy&rft_id=http%3A%2F%2Fplato.stanford.edu%2Fentries%2Fqt-measurement%2F&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal" class="Z3988">  </li> <li id="cite_note-Hilgevoord_2016-25"><a href="#cite_ref-Hilgevoord_2016_25-0">^</a> <cite class="citation web">Jan Hilgevoord; Jos Uffink. <a rel="nofollow" class="external text" href="http://plato.stanford.edu/entries/qt-uncertainty/">The Uncertainty Principle</a>. Stanford Encyclopedia of Philosophy. 12 July 2016 [2016-09-23]. （原始内容<a rel="nofollow" class="external text" href="https://web.archive.org/web/20131202050531/http://plato.stanford.edu/entries/qt-uncertainty/">存档</a>于2013-12-02）.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6&rft.atitle=The+Uncertainty+Principle&rft.au=Jan+Hilgevoord&rft.au=Jos+Uffink&rft.date=2016-07-12&rft.genre=unknown&rft.jtitle=Stanford+Encyclopedia+of+Philosophy&rft_id=http%3A%2F%2Fplato.stanford.edu%2Fentries%2Fqt-uncertainty%2F&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal" class="Z3988">  </li> <li id="cite_note-Braginsky1995-26"><a href="#cite_ref-Braginsky1995_26-0">^</a> <cite class="citation book">Vladimir B. Braginsky; Farid Ya Khalili. Quantum Measurement. Cambridge University Press. 25 May 1995. <a href="/wiki/Special:%E7%BD%91%E7%BB%9C%E4%B9%A6%E6%BA%90/978-0-521-48413-8" title="Special:网络书源/978-0-521-48413-8">ISBN 978-0-521-48413-8</a>.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6&rft.au=Farid+Ya+Khalili&rft.au=Vladimir+B.+Braginsky&rft.btitle=Quantum+Measurement&rft.date=1995-05-25&rft.genre=book&rft.isbn=978-0-521-48413-8&rft.pub=Cambridge+University+Press&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988">  </li> <li id="cite_note-Joos2003-29">^ <a href="#cite_ref-Joos2003_29-0">24.0</a> <a href="#cite_ref-Joos2003_29-1">24.1</a> <cite class="citation book">E. Joos; et al. <a rel="nofollow" class="external text" href="https://archive.org/details/decoherenceappea0000unse">Decoherence and the Appearance of a Classical World in Quantum Theory</a>. Springer. 2003. <a href="/wiki/Special:%E7%BD%91%E7%BB%9C%E4%B9%A6%E6%BA%90/3-540-00390-8" title="Special:网络书源/3-540-00390-8">ISBN 3-540-00390-8</a>.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6&rft.au=E.+Joos&rft.btitle=Decoherence+and+the+Appearance+of+a+Classical+World+in+Quantum+Theory&rft.date=2003&rft.genre=book&rft.isbn=3-540-00390-8&rft.pub=Springer&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fdecoherenceappea0000unse&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988">  引文格式1维护：显式使用等标签 (<a href="/wiki/Category:%E5%BC%95%E6%96%87%E6%A0%BC%E5%BC%8F1%E7%BB%B4%E6%8A%A4%EF%BC%9A%E6%98%BE%E5%BC%8F%E4%BD%BF%E7%94%A8%E7%AD%89%E6%A0%87%E7%AD%BE" title="Category:引文格式1维护：显式使用等标签">link</a>) </li> <li id="cite_note-Schlosshauer2004-30"><a href="#cite_ref-Schlosshauer2004_30-0">^</a> <cite class="citation journal">Schlosshauer, Maximilian. <a rel="nofollow" class="external text" href="https://archive.org/details/arxiv-quant-ph0312059">"Decoherence, the Measurement Problem, and Interpretations of Quantum Mechanics"</a>. Reviews of Modern Physics. 2005-06-28, (76(2004), 1267–1305). <a rel="nofollow" class="external text" href="//arxiv.org/abs/quant-ph/0312059">arXiv:quant-ph/0312059</a> <img alt="可免费查阅" src="//upload.wikimedia.org/wikipedia/commons/thumb/6/65/Lock-green.svg/9px-Lock-green.svg.png" decoding="async" width="9" height="14" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/65/Lock-green.svg/14px-Lock-green.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/65/Lock-green.svg/18px-Lock-green.svg.png 2x" data-file-width="512" data-file-height="813" />.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6&rft.atitle=%22Decoherence%2C+the+Measurement+Problem%2C+and+Interpretations+of+Quantum+Mechanics%22&rft.au=Schlosshauer%2C+Maximilian&rft.date=2005-06-28&rft.genre=article&rft.issue=76%282004%29%2C+1267%E2%80%931305&rft.jtitle=Reviews+of+Modern+Physics&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Farxiv-quant-ph0312059&rft_id=info%3Aarxiv%2Fquant-ph%2F0312059&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal" class="Z3988">  </li> <li id="cite_note-31"><a href="#cite_ref-31">^</a> <cite id="CITEREFZurek2002" class="citation">Zurek, Wojciech, <a rel="nofollow" class="external text" href="http://arxiv.org/abs/quant-ph/0306072">Decoherence and the Transition from Quantum to Classical—Revisited</a>, Los Alamos Science, 2002, 27 [2014-09-26], （原始内容<a rel="nofollow" class="external text" href="https://web.archive.org/web/20160201065420/http://arxiv.org/abs/quant-ph/0306072">存档</a>于2016-02-01）</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6&rft.atitle=Decoherence+and+the+Transition+from+Quantum+to+Classical%E2%80%94Revisited&rft.aufirst=Wojciech&rft.aulast=Zurek&rft.date=2002&rft.genre=article&rft.jtitle=Los+Alamos+Science&rft.volume=27&rft_id=http%3A%2F%2Farxiv.org%2Fabs%2Fquant-ph%2F0306072&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal" class="Z3988">  </li> <li id="cite_note-Joas-32"><a href="#cite_ref-Joas_32-0">^</a> <cite class="citation journal">Joas, Christian; Lehner, Christoph. <a rel="nofollow" class="external text" href="http://quantum-history.mpiwg-berlin.mpg.de/eLibrary/fileserverPub/Joas-Lehner_2009_Optical-mechanical.pdf/V1_Joas-Lehner_2009_Optical-mechanical.pdf">The classical roots of wave mechanics: Schrödinger's transformations of the optical-mechanical analogy</a> (PDF). Studies in History and Philosophy of Modern Physics. 2009, 40 (4): 338–351 [2014-09-28]. <a rel="nofollow" class="external text" href="//www.worldcat.org/issn/1355-2198">ISSN 1355-2198</a>. （原始内容<a rel="nofollow" class="external text" href="https://web.archive.org/web/20130709010423/http://quantum-history.mpiwg-berlin.mpg.de/eLibrary/fileserverPub/Joas-Lehner_2009_Optical-mechanical.pdf/V1_Joas-Lehner_2009_Optical-mechanical.pdf">存档</a> (PDF)于2013-07-09）.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6&rft.atitle=The+classical+roots+of+wave+mechanics%3A+Schr%C3%B6dinger%27s+transformations+of+the+optical-mechanical+analogy&rft.au=Lehner%2C+Christoph&rft.aufirst=Christian&rft.aulast=Joas&rft.date=2009&rft.genre=article&rft.issn=1355-2198&rft.issue=4&rft.jtitle=Studies+in+History+and+Philosophy+of+Modern+Physics&rft.pages=338-351&rft.volume=40&rft_id=http%3A%2F%2Fquantum-history.mpiwg-berlin.mpg.de%2FeLibrary%2FfileserverPub%2FJoas-Lehner_2009_Optical-mechanical.pdf%2FV1_Joas-Lehner_2009_Optical-mechanical.pdf&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal" class="Z3988">  </li> <li id="cite_note-Muynck2002-33">^ <a href="#cite_ref-Muynck2002_33-0">28.0</a> <a href="#cite_ref-Muynck2002_33-1">28.1</a> <cite class="citation book">W.M. de Muynck. Foundations of Quantum Mechanics, an Empiricist Approach. Springer Science & Business Media. 30 September 2002. <a href="/wiki/Special:%E7%BD%91%E7%BB%9C%E4%B9%A6%E6%BA%90/978-1-4020-0932-7" title="Special:网络书源/978-1-4020-0932-7">ISBN 978-1-4020-0932-7</a>.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6&rft.au=W.M.+de+Muynck&rft.btitle=Foundations+of+Quantum+Mechanics%2C+an+Empiricist+Approach&rft.date=2002-09-30&rft.genre=book&rft.isbn=978-1-4020-0932-7&rft.pub=Springer+Science+%26+Business+Media&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988">  </li> <li id="cite_note-Nielsen1976-34"><a href="#cite_ref-Nielsen1976_34-0">^</a> <cite class="citation book">J.R. Nielsen. The Correspondence Principle (1918 - 1923). Elsevier. 1 January 1976. <a href="/wiki/Special:%E7%BD%91%E7%BB%9C%E4%B9%A6%E6%BA%90/978-0-08-087101-1" title="Special:网络书源/978-0-08-087101-1">ISBN 978-0-08-087101-1</a>.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6&rft.au=J.R.+Nielsen&rft.btitle=The+Correspondence+Principle+%281918+-+1923%29&rft.date=1976-01-01&rft.genre=book&rft.isbn=978-0-08-087101-1&rft.pub=Elsevier&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988">  使用<code style="color:inherit; border:inherit; padding:inherit;">|accessdate=</code>需要含有<code style="color:inherit; border:inherit; padding:inherit;">|url=</code> (<a href="/wiki/Help:%E5%BC%95%E6%96%87%E6%A0%BC%E5%BC%8F1%E9%94%99%E8%AF%AF#accessdate_missing_url" title="Help:引文格式1错误">帮助</a>) </li> <li id="cite_note-Haroche-35">^ <a href="#cite_ref-Haroche_35-0">30.0</a> <a href="#cite_ref-Haroche_35-1">30.1</a> <a href="#cite_ref-Haroche_35-2">30.2</a> <a href="#cite_ref-Haroche_35-3">30.3</a> <cite class="citation book">Haroche, Serge; Raimond, Jean-Michel. <a rel="nofollow" class="external text" href="https://archive.org/details/exploringquantum0000haro">Exploring the Quantum: Atoms, Cavities, and Photons</a> 1st. Oxford University Press. 2006. <a href="/wiki/Special:%E7%BD%91%E7%BB%9C%E4%B9%A6%E6%BA%90/978-0198509141" title="Special:网络书源/978-0198509141">ISBN 978-0198509141</a>.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6&rft.au=Raimond%2C+Jean-Michel&rft.aufirst=Serge&rft.aulast=Haroche&rft.btitle=Exploring+the+Quantum%3A+Atoms%2C+Cavities%2C+and+Photons&rft.date=2006&rft.edition=1st&rft.genre=book&rft.isbn=978-0198509141&rft.pub=Oxford+University+Press&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fexploringquantum0000haro&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988">  </li> <li id="cite_note-36"><a href="#cite_ref-36">^</a> <cite class="citation web"><a rel="nofollow" class="external text" href="http://philsci-archive.pitt.edu/2328/1/handbook.pdf">Between classical and quantum</a> (PDF). [2012-08-19]. （原始内容<a rel="nofollow" class="external text" href="https://web.archive.org/web/20210225203130/http://philsci-archive.pitt.edu/2328/1/handbook.pdf">存档</a> (PDF)于2021-02-25）.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6&rft.btitle=Between+classical+and+quantum&rft.genre=unknown&rft_id=http%3A%2F%2Fphilsci-archive.pitt.edu%2F2328%2F1%2Fhandbook.pdf&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988">  </li> <li id="cite_note-feynbook-37"><a href="#cite_ref-feynbook_37-0">^</a> <cite class="citation book"><a href="/wiki/Richard_Feynman" class="mw-redirect" title="Richard Feynman">Feynman, Richard</a>. QED: The Strange Theory of Light and Matter. Princeton University Press. 1985. <a href="/wiki/Special:%E7%BD%91%E7%BB%9C%E4%B9%A6%E6%BA%90/978-0-691-12575-6" title="Special:网络书源/978-0-691-12575-6">ISBN 978-0-691-12575-6</a>.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6&rft.aufirst=Richard&rft.aulast=Feynman&rft.btitle=QED%3A+The+Strange+Theory+of+Light+and+Matter&rft.date=1985&rft.genre=book&rft.isbn=978-0-691-12575-6&rft.pub=Princeton+University+Press&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988">  </li> <li id="cite_note-38"><a href="#cite_ref-38">^</a> <cite class="citation journal">Smolin, Lee. Three Roads to Quantum Gravity: 129–148. 2001. <a href="/wiki/Special:%E7%BD%91%E7%BB%9C%E4%B9%A6%E6%BA%90/0-465-07835-4" title="Special:网络书源/0-465-07835-4">ISBN 0-465-07835-4</a>.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6&rft.atitle=Three+Roads+to+Quantum+Gravity&rft.aufirst=Lee&rft.aulast=Smolin&rft.date=2001&rft.genre=article&rft.isbn=0-465-07835-4&rft.pages=129-148&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal" class="Z3988">  </li> <li id="cite_note-39"><a href="#cite_ref-39">^</a> <cite id="CITEREFKiefer2005" class="citation journal">Kiefer, Claus. Quantum Gravity: General Introduction and Recent Developments. <a href="/wiki/Annalen_der_Physik" class="mw-redirect" title="Annalen der Physik">Annalen der Physik</a>. 2005, 15: 129–148. <a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2006AnP...518..129K">Bibcode:2006AnP...518..129K</a>. <a rel="nofollow" class="external text" href="//arxiv.org/abs/gr-qc/0508120">arXiv:gr-qc/0508120</a> <img alt="可免费查阅" src="//upload.wikimedia.org/wikipedia/commons/thumb/6/65/Lock-green.svg/9px-Lock-green.svg.png" decoding="async" width="9" height="14" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/65/Lock-green.svg/14px-Lock-green.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/65/Lock-green.svg/18px-Lock-green.svg.png 2x" data-file-width="512" data-file-height="813" />. <a rel="nofollow" class="external text" href="https://doi.org/10.1002%2Fandp.200510175">doi:10.1002/andp.200510175</a>.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6&rft.atitle=Quantum+Gravity%3A+General+Introduction+and+Recent+Developments&rft.aufirst=Claus&rft.aulast=Kiefer&rft.date=2005&rft.genre=article&rft.jtitle=Annalen+der+Physik&rft.pages=129-148&rft.volume=15&rft_id=info%3Aarxiv%2Fgr-qc%2F0508120&rft_id=info%3Abibcode%2F2006AnP...518..129K&rft_id=info%3Adoi%2F10.1002%2Fandp.200510175&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal" class="Z3988">  </li> <li id="cite_note-40"><a href="#cite_ref-40">^</a> <cite class="citation book">曾谨言. 量子力学教程：量子力学百年. 科学出版社. : ix-xxi. <a href="/wiki/Special:%E7%BD%91%E7%BB%9C%E4%B9%A6%E6%BA%90/7-03-010982-1" title="Special:网络书源/7-03-010982-1">ISBN 7-03-010982-1</a>.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6&rft.au=%E6%9B%BE%E8%B0%A8%E8%A8%80&rft.btitle=%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6%E6%95%99%E7%A8%8B%EF%BC%9A%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6%E7%99%BE%E5%B9%B4&rft.genre=book&rft.isbn=7-03-010982-1&rft.pages=ix-xxi&rft.pub=%E7%A7%91%E5%AD%A6%E5%87%BA%E7%89%88%E7%A4%BE&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988">  </li> <li id="cite_note-42"><a href="#cite_ref-42">^</a> The Character of Physical Law (1965) Ch. 6; also quoted in The New Quantum Universe (2003), by Tony Hey and Patrick Walters </li> <li id="cite_note-43"><a href="#cite_ref-43">^</a> Weinberg, S. <a rel="nofollow" class="external text" href="http://arxiv.org/abs/1109.6462">"Collapse of the State Vector"</a> （<a rel="nofollow" class="external text" href="//web.archive.org/web/20210508112022/http://arxiv.org/abs/1109.6462">页面存档备份</a>，存于<a href="/wiki/%E4%BA%92%E8%81%94%E7%BD%91%E6%A1%A3%E6%A1%88%E9%A6%86" title="互联网档案馆">互联网档案馆</a>）, Phys. Rev. A 85, 062116 (2012). </li> <li id="cite_note-Bell1964-44"><a href="#cite_ref-Bell1964_44-0">^</a> Bell, John. On the Einstein Podolsky Rosen Paradox, Physics 1 3, 195-200, Nov. 1964 </li> <li id="cite_note-Aspect1999-45"><a href="#cite_ref-Aspect1999_45-0">^</a> <cite class="citation journal">Aspect A. Bell's inequality test: more ideal than ever. Nature. 1999-03-18, 398 (6724): 189–90. <a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1999Natur.398..189A">Bibcode:1999Natur.398..189A</a>. <a rel="nofollow" class="external text" href="https://doi.org/10.1038%2F18296">doi:10.1038/18296</a>.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6&rft.atitle=Bell%27s+inequality+test%3A+more+ideal+than+ever&rft.au=Aspect+A&rft.date=1999-03-18&rft.genre=article&rft.issue=6724&rft.jtitle=Nature&rft.pages=189-90&rft.volume=398&rft_id=info%3Abibcode%2F1999Natur.398..189A&rft_id=info%3Adoi%2F10.1038%2F18296&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal" class="Z3988">  使用<code style="color:inherit; border:inherit; padding:inherit;">|accessdate=</code>需要含有<code style="color:inherit; border:inherit; padding:inherit;">|url=</code> (<a href="/wiki/Help:%E5%BC%95%E6%96%87%E6%A0%BC%E5%BC%8F1%E9%94%99%E8%AF%AF#accessdate_missing_url" title="Help:引文格式1错误">帮助</a>) </li> <li id="cite_note-46"><a href="#cite_ref-46">^</a> <cite class="citation web"><a rel="nofollow" class="external text" href="http://plato.stanford.edu/entries/qm-action-distance/">Action at a Distance in Quantum Mechanics (Stanford Encyclopedia of Philosophy)</a>. Plato.stanford.edu. 2007-01-26 [2012-08-18]. （原始内容<a rel="nofollow" class="external text" href="https://web.archive.org/web/20210508112028/https://plato.stanford.edu/entries/qm-action-distance/">存档</a>于2021-05-08）.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6&rft.btitle=Action+at+a+Distance+in+Quantum+Mechanics+%28Stanford+Encyclopedia+of+Philosophy%29&rft.date=2007-01-26&rft.genre=unknown&rft.pub=Plato.stanford.edu&rft_id=http%3A%2F%2Fplato.stanford.edu%2Fentries%2Fqm-action-distance%2F&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988">  </li> <li id="cite_note-47"><a href="#cite_ref-47">^</a> <cite class="citation book">Everett, Hugh. <a rel="nofollow" class="external text" href="http://www.pbs.org/wgbh/nova/manyworlds/pdf/dissertation.pdf">Theory of the Universal Wavefunction</a> (PDF). Princeton University. 1956, 1973: 1-140 [2012-07-16]. （原始内容<a rel="nofollow" class="external text" href="https://web.archive.org/web/20121016151021/http://www.pbs.org/wgbh/nova/manyworlds/pdf/dissertation.pdf">存档</a> (PDF)于2012-10-16）.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6&rft.aufirst=Hugh&rft.aulast=Everett&rft.btitle=Theory+of+the+Universal+Wavefunction&rft.genre=book&rft.pages=1-140&rft.pub=Princeton+University&rft_id=http%3A%2F%2Fwww.pbs.org%2Fwgbh%2Fnova%2Fmanyworlds%2Fpdf%2Fdissertation.pdf&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988">  请检查<code style="color:inherit; border:inherit; padding:inherit;">|date=</code>中的日期值 (<a href="/wiki/Help:%E5%BC%95%E6%96%87%E6%A0%BC%E5%BC%8F1%E9%94%99%E8%AF%AF#bad_date" title="Help:引文格式1错误">帮助</a>) </li> <li id="cite_note-48"><a href="#cite_ref-48">^</a> <cite class="citation journal">Everett, Hugh. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20111027191052/http://www.univer.omsk.su/omsk/Sci/Everett/paper1957.html">Relative State Formulation of Quantum Mechanics</a>. Reviews of Modern Physics. 1957, 29: 454–462. <a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1957RvMP...29..454E">Bibcode:1957RvMP...29..454E</a>. <a rel="nofollow" class="external text" href="https://doi.org/10.1103%2FRevModPhys.29.454">doi:10.1103/RevModPhys.29.454</a>. （<a rel="nofollow" class="external text" href="http://www.univer.omsk.su/omsk/Sci/Everett/paper1957.html">原始内容</a>存档于2011年10月27日）.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6&rft.atitle=Relative+State+Formulation+of+Quantum+Mechanics&rft.aufirst=Hugh&rft.aulast=Everett&rft.date=1957&rft.genre=article&rft.jtitle=Reviews+of+Modern+Physics&rft.pages=454-462&rft.volume=29&rft_id=http%3A%2F%2Fwww.univer.omsk.su%2Fomsk%2FSci%2FEverett%2Fpaper1957.html&rft_id=info%3Abibcode%2F1957RvMP...29..454E&rft_id=info%3Adoi%2F10.1103%2FRevModPhys.29.454&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal" class="Z3988">  </li> <li id="cite_note-zeh-49"><a href="#cite_ref-zeh_49-0">^</a> H. Dieter Zeh, <a rel="nofollow" class="external text" href="http://www.rzuser.uni-heidelberg.de/~as3/FP70.pdf">On the Interpretation of Measurement in Quantum Theory</a> （<a rel="nofollow" class="external text" href="//web.archive.org/web/20210304060505/http://www.rzuser.uni-heidelberg.de/~as3/FP70.pdf">页面存档备份</a>，存于<a href="/wiki/%E4%BA%92%E8%81%94%E7%BD%91%E6%A1%A3%E6%A1%88%E9%A6%86" title="互联网档案馆">互联网档案馆</a>）, Foundation of Physics, vol. 1, pp. 69–76, (1970). </li> <li id="cite_note-50"><a href="#cite_ref-50">^</a> <cite class="citation journal">Bohm, David. A Suggested Interpretation of the Quantum Theory in Terms of "Hidden Variables" I. Physical Review. 1952, 85: 166–179. <a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1952PhRv...85..166B">Bibcode:1952PhRv...85..166B</a>. <a rel="nofollow" class="external text" href="https://doi.org/10.1103%2FPhysRev.85.166">doi:10.1103/PhysRev.85.166</a>.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6&rft.atitle=A+Suggested+Interpretation+of+the+Quantum+Theory+in+Terms+of+%22Hidden+Variables%22+I&rft.aufirst=David&rft.aulast=Bohm&rft.date=1952&rft.genre=article&rft.jtitle=Physical+Review&rft.pages=166-179&rft.volume=85&rft_id=info%3Abibcode%2F1952PhRv...85..166B&rft_id=info%3Adoi%2F10.1103%2FPhysRev.85.166&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal" class="Z3988">  </li> <li id="cite_note-51"><a href="#cite_ref-51">^</a> <cite class="citation journal">Bohm, David. A Suggested Interpretation of the Quantum Theory in Terms of "Hidden Variables", II. Physical Review. 1952, 85: 180–193. <a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1952PhRv...85..180B">Bibcode:1952PhRv...85..180B</a>. <a rel="nofollow" class="external text" href="https://doi.org/10.1103%2FPhysRev.85.180">doi:10.1103/PhysRev.85.180</a>.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6&rft.atitle=A+Suggested+Interpretation+of+the+Quantum+Theory+in+Terms+of+%22Hidden+Variables%22%2C+II&rft.aufirst=David&rft.aulast=Bohm&rft.date=1952&rft.genre=article&rft.jtitle=Physical+Review&rft.pages=180-193&rft.volume=85&rft_id=info%3Abibcode%2F1952PhRv...85..180B&rft_id=info%3Adoi%2F10.1103%2FPhysRev.85.180&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal" class="Z3988">  </li> <li id="cite_note-52"><a href="#cite_ref-52">^</a> <cite class="citation web">張守進尤信介. <a rel="nofollow" class="external text" href="https://scitechvista.nat.gov.tw/zh-tw/articles/c/5/1/10/62/172.htm">光電科技：現代的電光石火</a>. 科技部. [2016-09-22]. （原始内容<a rel="nofollow" class="external text" href="https://web.archive.org/web/20210508112051/https://scitechvista.nat.gov.tw/zh-tw/articles/c/5/1/10/62/172.htm">存档</a>于2021-05-08）. <q>由於發光二極體有這麼多優良的特性，因此在我們日常生活中的使用已經越來越普遍。.</q></cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6&rft.au=%E5%BC%B5%E5%AE%88%E9%80%B2+%E5%B0%A4%E4%BF%A1%E4%BB%8B&rft.btitle=%E5%85%89%E9%9B%BB%E7%A7%91%E6%8A%80%EF%BC%9A%E7%8F%BE%E4%BB%A3%E7%9A%84%E9%9B%BB%E5%85%89%E7%9F%B3%E7%81%AB&rft.genre=unknown&rft.pub=%E7%A7%91%E6%8A%80%E9%83%A8&rft_id=https%3A%2F%2Fscitechvista.nat.gov.tw%2Fzh-tw%2Farticles%2Fc%2F5%2F1%2F10%2F62%2F172.htm&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988">  </li> <li id="cite_note-53"><a href="#cite_ref-53">^</a> <cite class="citation web">Seabaugh, Alan. <a rel="nofollow" class="external text" href="http://spectrum.ieee.org/semiconductors/devices/the-tunneling-transistor">The Tunneling Transistor</a>. IEEE Spectrum. 30 Sep 2013 [2016-09-21]. （原始内容<a rel="nofollow" class="external text" href="https://web.archive.org/web/20210508112051/https://spectrum.ieee.org/semiconductors/devices/the-tunneling-transistor">存档</a>于2021-05-08）. <q>The flash memory inside our USB sticks, cellphones, and other gadgets uses tunneling to inject electrons across oxide barriers into charge-trapping regions.</q></cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6&rft.aufirst=Alan&rft.aulast=Seabaugh&rft.btitle=The+Tunneling+Transistor&rft.date=2013-09-30&rft.genre=unknown&rft.pub=IEEE+Spectrum&rft_id=http%3A%2F%2Fspectrum.ieee.org%2Fsemiconductors%2Fdevices%2Fthe-tunneling-transistor&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988">  </li> <li id="cite_note-dpf99-54"><a href="#cite_ref-dpf99_54-0">^</a> <cite class="citation conference">White, M. Anisotropies in the CMB. Proceedings of the Los Angeles Meeting, DPF 99. UCLA. 1999. <a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1999dpf..conf.....W">Bibcode:1999dpf..conf.....W</a>. <a rel="nofollow" class="external text" href="//arxiv.org/abs/astro-ph/9903232">arXiv:astro-ph/9903232</a> <img alt="可免费查阅" src="//upload.wikimedia.org/wikipedia/commons/thumb/6/65/Lock-green.svg/9px-Lock-green.svg.png" decoding="async" width="9" height="14" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/65/Lock-green.svg/14px-Lock-green.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/65/Lock-green.svg/18px-Lock-green.svg.png 2x" data-file-width="512" data-file-height="813" />.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6&rft.aufirst=M.&rft.aulast=White&rft.btitle=Proceedings+of+the+Los+Angeles+Meeting%2C+DPF+99&rft.date=1999&rft.genre=conference&rft.pub=UCLA&rft_id=info%3Aarxiv%2Fastro-ph%2F9903232&rft_id=info%3Abibcode%2F1999dpf..conf.....W&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988">  使用<code style="color:inherit; border:inherit; padding:inherit;">|accessdate=</code>需要含有<code style="color:inherit; border:inherit; padding:inherit;">|url=</code> (<a href="/wiki/Help:%E5%BC%95%E6%96%87%E6%A0%BC%E5%BC%8F1%E9%94%99%E8%AF%AF#accessdate_missing_url" title="Help:引文格式1错误">帮助</a>) </li> <li id="cite_note-Basdevant2007-55"><a href="#cite_ref-Basdevant2007_55-0">^</a> <cite class="citation book">Jean-Louis Basdevant. Lectures on Quantum Mechanics. Springer Science & Business Media. <a href="/wiki/Special:%E7%BD%91%E7%BB%9C%E4%B9%A6%E6%BA%90/978-0-387-37744-5" title="Special:网络书源/978-0-387-37744-5">ISBN 978-0-387-37744-5</a>.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6&rft.au=Jean-Louis+Basdevant&rft.btitle=Lectures+on+Quantum+Mechanics&rft.genre=book&rft.isbn=978-0-387-37744-5&rft.pub=Springer+Science+%26+Business+Media&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988">  </li> <li id="cite_note-Ryden2003-56"><a href="#cite_ref-Ryden2003_56-0">^</a> <cite class="citation book">Barbara Sue Ryden. <a rel="nofollow" class="external text" href="https://archive.org/details/introductiontoco0000ryde">Introduction to cosmology</a>. Addison-Wesley. 2003. <a href="/wiki/Special:%E7%BD%91%E7%BB%9C%E4%B9%A6%E6%BA%90/978-0-8053-8912-8" title="Special:网络书源/978-0-8053-8912-8">ISBN 978-0-8053-8912-8</a>.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6&rft.au=Barbara+Sue+Ryden&rft.btitle=Introduction+to+cosmology&rft.date=2003&rft.genre=book&rft.isbn=978-0-8053-8912-8&rft.pub=Addison-Wesley&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fintroductiontoco0000ryde&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988">  </li> <li id="cite_note-Bojowald2012-57"><a href="#cite_ref-Bojowald2012_57-0">^</a> <cite class="citation book">Martin Bojowald. The Universe: A View from Classical and Quantum Gravity. John Wiley & Sons. 5 November 2012. <a href="/wiki/Special:%E7%BD%91%E7%BB%9C%E4%B9%A6%E6%BA%90/978-3-527-66769-7" title="Special:网络书源/978-3-527-66769-7">ISBN 978-3-527-66769-7</a>.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6&rft.au=Martin+Bojowald&rft.btitle=The+Universe%3A+A+View+from+Classical+and+Quantum+Gravity&rft.date=2012-11-05&rft.genre=book&rft.isbn=978-3-527-66769-7&rft.pub=John+Wiley+%26+Sons&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988">  </li> <li id="cite_note-OxtobyGillis2011-58">^ <a href="#cite_ref-OxtobyGillis2011_58-0">52.0</a> <a href="#cite_ref-OxtobyGillis2011_58-1">52.1</a> <a href="#cite_ref-OxtobyGillis2011_58-2">52.2</a> <cite class="citation book">David W. Oxtoby; H. Pat Gillis; Alan Campion. Principles of Modern Chemistry, 7th ed.. Cengage Learning. May 2011. <a href="/wiki/Special:%E7%BD%91%E7%BB%9C%E4%B9%A6%E6%BA%90/978-0-8400-4931-5" title="Special:网络书源/978-0-8400-4931-5">ISBN 978-0-8400-4931-5</a>.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6&rft.au=Alan+Campion&rft.au=David+W.+Oxtoby&rft.au=H.+Pat+Gillis&rft.btitle=Principles+of+Modern+Chemistry%2C+7th+ed.&rft.date=2011-05&rft.genre=book&rft.isbn=978-0-8400-4931-5&rft.pub=Cengage+Learning&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988">  使用<code style="color:inherit; border:inherit; padding:inherit;">|accessdate=</code>需要含有<code style="color:inherit; border:inherit; padding:inherit;">|url=</code> (<a href="/wiki/Help:%E5%BC%95%E6%96%87%E6%A0%BC%E5%BC%8F1%E9%94%99%E8%AF%AF#accessdate_missing_url" title="Help:引文格式1错误">帮助</a>) </li> <li id="cite_note-FeynmanPhys-59"><a href="#cite_ref-FeynmanPhys_59-0">^</a> <cite class="citation book">Richard P. Feynman; Robert B. Leighton; Matthew Sands. <a href="/wiki/%E8%B4%B9%E6%9B%BC%E7%89%A9%E7%90%86%E5%AD%A6%E8%AE%B2%E4%B9%89" title="费曼物理学讲义">The Feynman Lectures on Physics</a> 1. Addison–Wesley. 1964: 2–8. <a href="/wiki/Special:%E7%BD%91%E7%BB%9C%E4%B9%A6%E6%BA%90/0-201-02115-3" title="Special:网络书源/0-201-02115-3">ISBN 0-201-02115-3</a>.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6&rft.au=Matthew+Sands&rft.au=Richard+P.+Feynman&rft.au=Robert+B.+Leighton&rft.btitle=The+Feynman+Lectures+on+Physics&rft.date=1964&rft.genre=book&rft.isbn=0-201-02115-3&rft.pages=2-8&rft.pub=Addison%E2%80%93Wesley&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988">  </li> <li id="cite_note-NielsenChuang2010-60"><a href="#cite_ref-NielsenChuang2010_60-0">^</a> <cite class="citation book">Michael A. Nielsen; Isaac L. Chuang. Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press. 9 December 2010. <a href="/wiki/Special:%E7%BD%91%E7%BB%9C%E4%B9%A6%E6%BA%90/978-1-139-49548-6" title="Special:网络书源/978-1-139-49548-6">ISBN 978-1-139-49548-6</a>.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6&rft.au=Isaac+L.+Chuang&rft.au=Michael+A.+Nielsen&rft.btitle=Quantum+Computation+and+Quantum+Information%3A+10th+Anniversary+Edition&rft.date=2010-12-09&rft.genre=book&rft.isbn=978-1-139-49548-6&rft.pub=Cambridge+University+Press&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988">  使用<code style="color:inherit; border:inherit; padding:inherit;">|accessdate=</code>需要含有<code style="color:inherit; border:inherit; padding:inherit;">|url=</code> (<a href="/wiki/Help:%E5%BC%95%E6%96%87%E6%A0%BC%E5%BC%8F1%E9%94%99%E8%AF%AF#accessdate_missing_url" title="Help:引文格式1错误">帮助</a>) </li> </ol></div> <div class="mw-heading mw-heading2"><h2 id="外部链接">外部链接</h2>[<a href="/w/index.php?title=%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6&action=edit&section=31" title="编辑章节：外部链接">编辑</a>]</div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r82655521"><style data-mw-deduplicate="TemplateStyles:r83112147">.mw-parser-output .sister-box .side-box-abovebelow{padding:0.75em 0;text-align:center}.mw-parser-output .sister-box .side-box-abovebelow>b{display:block}.mw-parser-output .sister-box .side-box-text>ul{border-top:1px solid #aaa;padding:0.75em 0;width:217px;margin:0 auto}.mw-parser-output .sister-box .side-box-text>ul>li{min-height:31px}.mw-parser-output .sister-logo{display:inline-block;width:31px;line-height:31px;vertical-align:middle;text-align:center}.mw-parser-output .sister-link{display:inline-block;margin-left:4px;width:182px;vertical-align:middle}</style><div role="navigation" aria-labelledby="sister-projects" class="side-box metadata side-box-right sister-box sistersitebox plainlinks"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r82655520"> <div class="side-box-abovebelow"> 量子力学在维基百科的<a href="/wiki/Wikipedia:%E7%BB%B4%E5%9F%BA%E5%AA%92%E4%BD%93%E5%A7%8A%E5%A6%B9%E9%A1%B9%E7%9B%AE" title="Wikipedia:维基媒体姊妹项目">姊妹项目</a></div> <div class="side-box-flex"> <div class="side-box-text plainlist"><ul><li><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/e/ec/Wiktionary-logo.svg/27px-Wiktionary-logo.svg.png" decoding="async" width="27" height="26" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/ec/Wiktionary-logo.svg/41px-Wiktionary-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/ec/Wiktionary-logo.svg/54px-Wiktionary-logo.svg.png 2x" data-file-width="370" data-file-height="350" />维基词典上的<a href="https://zh.wiktionary.org/wiki/Special:Search/%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6" class="extiw" title="wikt:Special:Search/量子力学">字词解释</a></li><li><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/20px-Commons-logo.svg.png" decoding="async" width="20" height="27" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/30px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/40px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" />维基共享资源上的<a href="https://commons.wikimedia.org/wiki/Category:Quantum_mechanics" class="extiw" title="c:Category:Quantum mechanics">多媒体资源</a></li><li><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/2/24/Wikinews-logo.svg/27px-Wikinews-logo.svg.png" decoding="async" width="27" height="15" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/24/Wikinews-logo.svg/41px-Wikinews-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/24/Wikinews-logo.svg/54px-Wikinews-logo.svg.png 2x" data-file-width="759" data-file-height="415" />维基新闻上的<a href="https://zh.wikinews.org/wiki/Special:Search/%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6" class="extiw" title="n:Special:Search/量子力学">新闻</a></li><li><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Wikiquote-logo.svg/23px-Wikiquote-logo.svg.png" decoding="async" width="23" height="27" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Wikiquote-logo.svg/35px-Wikiquote-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Wikiquote-logo.svg/46px-Wikiquote-logo.svg.png 2x" data-file-width="300" data-file-height="355" />维基语录上的<a href="https://zh.wikiquote.org/wiki/%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%B8" class="extiw" title="q:量子力學">名言</a></li><li><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Wikibooks-logo.svg/27px-Wikibooks-logo.svg.png" decoding="async" width="27" height="27" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Wikibooks-logo.svg/41px-Wikibooks-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Wikibooks-logo.svg/54px-Wikibooks-logo.svg.png 2x" data-file-width="300" data-file-height="300" />维基教科书上的<a href="https://zh.wikibooks.org/wiki/%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6" class="extiw" title="b:量子力学">教科书和手册</a></li><li><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/0/0b/Wikiversity_logo_2017.svg/27px-Wikiversity_logo_2017.svg.png" decoding="async" width="27" height="22" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/0b/Wikiversity_logo_2017.svg/41px-Wikiversity_logo_2017.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/0b/Wikiversity_logo_2017.svg/54px-Wikiversity_logo_2017.svg.png 2x" data-file-width="626" data-file-height="512" />维基学院上的<a href="https://zh.wikiversity.org/wiki/Special:Search/%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6" class="extiw" title="v:Special:Search/量子力学">学习资源</a></li></ul></div></div> </div> <ul><li><a href="/wiki/%E5%9B%BD%E7%AB%8B%E4%BA%A4%E9%80%9A%E5%A4%A7%E5%AD%A6" class="mw-redirect" title="国立交通大学">国立交通大学</a>物理系視聽教學：<a rel="nofollow" class="external text" href="http://ocw.nctu.edu.tw/course_detail.php?bgid=1&gid=3&nid=386#.VCuak4l0xwE">量子力学导论</a> （<a rel="nofollow" class="external text" href="//web.archive.org/web/20210508112113/http://ocw.nctu.edu.tw/course_detail.php?bgid=1&gid=3&nid=386#.VCuak4l0xwE">页面存档备份</a>，存于<a href="/wiki/%E4%BA%92%E8%81%94%E7%BD%91%E6%A1%A3%E6%A1%88%E9%A6%86" title="互联网档案馆">互联网档案馆</a>）。</li> <li>J. O'Connor and E. F. Robertson: <a rel="nofollow" class="external text" href="http://www-history.mcs.st-andrews.ac.uk/history/HistTopics/The_Quantum_age_begins.html">A history of quantum mechanics.</a> （<a rel="nofollow" class="external text" href="//web.archive.org/web/20110718113126/http://www-history.mcs.st-andrews.ac.uk/history/HistTopics/The_Quantum_age_begins.html">页面存档备份</a>，存于<a href="/wiki/%E4%BA%92%E8%81%94%E7%BD%91%E6%A1%A3%E6%A1%88%E9%A6%86" title="互联网档案馆">互联网档案馆</a>）</li> <li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20080913201312/http://www.quantiki.org/wiki/index.php/Introduction_to_Quantum_Theory">Introduction to Quantum Theory at Quantiki.</a></li> <li><a rel="nofollow" class="external text" href="http://bethe.cornell.edu/">Quantum Physics Made Relatively Simple</a> （<a rel="nofollow" class="external text" href="//web.archive.org/web/20110406121235/http://bethe.cornell.edu/">页面存档备份</a>，存于<a href="/wiki/%E4%BA%92%E8%81%94%E7%BD%91%E6%A1%A3%E6%A1%88%E9%A6%86" title="互联网档案馆">互联网档案馆</a>）: three video lectures by <a href="/wiki/Hans_Bethe" class="mw-redirect" title="Hans Bethe">Hans Bethe</a></li></ul> <dl><dt>课程材料</dt></dl> <ul><li><a rel="nofollow" class="external text" href="http://oyc.yale.edu/sites/default/files/notes_quantum_cookbook.pdf">Quantum Cook Book</a> （<a rel="nofollow" class="external text" href="//web.archive.org/web/20231010142610/http://oyc.yale.edu/sites/default/files/notes_quantum_cookbook.pdf">页面存档备份</a>，存于<a href="/wiki/%E4%BA%92%E8%81%94%E7%BD%91%E6%A1%A3%E6%A1%88%E9%A6%86" title="互联网档案馆">互联网档案馆</a>） and <a rel="nofollow" class="external text" href="http://oyc.yale.edu/physics/phys-201#sessions">PHYS 201: Fundamentals of Physics II</a> （<a rel="nofollow" class="external text" href="//web.archive.org/web/20231010141755/http://oyc.yale.edu/physics/phys-201#sessions">页面存档备份</a>，存于<a href="/wiki/%E4%BA%92%E8%81%94%E7%BD%91%E6%A1%A3%E6%A1%88%E9%A6%86" title="互联网档案馆">互联网档案馆</a>） by <a href="/wiki/%E6%8B%89%E9%A6%AC%E7%A9%86%E8%92%82%C2%B7%E5%B0%9A%E5%8D%A1%E7%88%BE" title="拉馬穆蒂·尚卡爾">Ramamurti Shankar</a>, Yale OpenCourseware</li> <li><a rel="nofollow" class="external text" href="http://www.lightandmatter.com/lm/">The Modern Revolution in Physics</a> （<a rel="nofollow" class="external text" href="//web.archive.org/web/20200601172955/http://www.lightandmatter.com/lm/">页面存档备份</a>，存于<a href="/wiki/%E4%BA%92%E8%81%94%E7%BD%91%E6%A1%A3%E6%A1%88%E9%A6%86" title="互联网档案馆">互联网档案馆</a>） – an online textbook.</li> <li><a href="/wiki/MIT_OpenCourseWare" title="MIT OpenCourseWare">MIT OpenCourseWare</a>: <a rel="nofollow" class="external text" href="https://ocw.mit.edu/courses/chemistry/">Chemistry</a> （<a rel="nofollow" class="external text" href="//web.archive.org/web/20220318131728/https://ocw.mit.edu/courses/chemistry/">页面存档备份</a>，存于<a href="/wiki/%E4%BA%92%E8%81%94%E7%BD%91%E6%A1%A3%E6%A1%88%E9%A6%86" title="互联网档案馆">互联网档案馆</a>） and <a rel="nofollow" class="external text" href="https://ocw.mit.edu/courses/physics/">Physics</a> （<a rel="nofollow" class="external text" href="//web.archive.org/web/20220315082844/https://ocw.mit.edu/courses/physics/">页面存档备份</a>，存于<a href="/wiki/%E4%BA%92%E8%81%94%E7%BD%91%E6%A1%A3%E6%A1%88%E9%A6%86" title="互联网档案馆">互联网档案馆</a>）. See <a rel="nofollow" class="external text" href="https://ocw.mit.edu/courses/physics/8-04-quantum-physics-i-spring-2016/">8.04</a> （<a rel="nofollow" class="external text" href="//web.archive.org/web/20220320114732/https://ocw.mit.edu/courses/physics/8-04-quantum-physics-i-spring-2016/">页面存档备份</a>，存于<a href="/wiki/%E4%BA%92%E8%81%94%E7%BD%91%E6%A1%A3%E6%A1%88%E9%A6%86" title="互联网档案馆">互联网档案馆</a>）, <a rel="nofollow" class="external text" href="https://ocw.mit.edu/courses/physics/8-05-quantum-physics-ii-fall-2013/index.htm">8.05</a> （<a rel="nofollow" class="external text" href="//web.archive.org/web/20210227101754/https://ocw.mit.edu/courses/physics/8-05-quantum-physics-ii-fall-2013/index.htm">页面存档备份</a>，存于<a href="/wiki/%E4%BA%92%E8%81%94%E7%BD%91%E6%A1%A3%E6%A1%88%E9%A6%86" title="互联网档案馆">互联网档案馆</a>） and <a rel="nofollow" class="external text" href="https://ocw.mit.edu/courses/physics/8-06-quantum-physics-iii-spring-2018/index.htm">8.06</a> （<a rel="nofollow" class="external text" href="//web.archive.org/web/20220116143557/https://ocw.mit.edu/courses/physics/8-06-quantum-physics-iii-spring-2018/index.htm">页面存档备份</a>，存于<a href="/wiki/%E4%BA%92%E8%81%94%E7%BD%91%E6%A1%A3%E6%A1%88%E9%A6%86" title="互联网档案馆">互联网档案馆</a>）</li> <li><a rel="nofollow" class="external text" href="http://www.physics.csbsju.edu/QM/">5½ Examples in Quantum Mechanics</a> （<a rel="nofollow" class="external text" href="//web.archive.org/web/20110725062349/http://www.physics.csbsju.edu/QM/">页面存档备份</a>，存于<a href="/wiki/%E4%BA%92%E8%81%94%E7%BD%91%E6%A1%A3%E6%A1%88%E9%A6%86" title="互联网档案馆">互联网档案馆</a>）</li> <li><a rel="nofollow" class="external text" href="http://www.imperial.ac.uk/quantuminformation/qi/tutorials">Imperial College Quantum Mechanics Course.</a> （<a rel="nofollow" class="external text" href="//web.archive.org/web/20110810075114/http://www.imperial.ac.uk/quantuminformation/qi/tutorials">页面存档备份</a>，存于<a href="/wiki/%E4%BA%92%E8%81%94%E7%BD%91%E6%A1%A3%E6%A1%88%E9%A6%86" title="互联网档案馆">互联网档案馆</a>）</li></ul> <dl><dt>哲学</dt></dl> <ul><li><cite class="citation encyclopaedia">Ismael, Jenann. <a rel="nofollow" class="external text" href="https://plato.stanford.edu/entries/qm/">Quantum Mechanics</a>. <a href="/wiki/%E7%88%B1%E5%BE%B7%E5%8D%8E%C2%B7%E6%89%8E%E5%B0%94%E5%A1%94" title="爱德华·扎尔塔">扎尔塔, 爱德华·N</a> (编). 《<a href="/wiki/%E5%8F%B2%E4%B8%B9%E4%BD%9B%E5%93%B2%E5%AD%B8%E7%99%BE%E7%A7%91%E5%85%A8%E6%9B%B8" title="史丹佛哲學百科全書">斯坦福哲学百科全书</a>》.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6&rft.atitle=Quantum+Mechanics&rft.aufirst=Jenann&rft.aulast=Ismael&rft.btitle=%E3%80%8A-%7Bzh-hans%3A%E6%96%AF%E5%9D%A6%E7%A6%8F%3B+zh-tw%3A%E5%8F%B2%E4%B8%B9%E4%BD%9B%3Bzh-mo%3A%E5%8F%B2%E4%B8%B9%E7%A6%8F%3Bzh-hk%3A%E5%8F%B2%E4%B8%B9%E7%A6%8F%7D-%E5%93%B2%E5%AD%A6%E7%99%BE%E7%A7%91%E5%85%A8%E4%B9%A6%E3%80%8B&rft.genre=bookitem&rft_id=https%3A%2F%2Fplato.stanford.edu%2Fentries%2Fqm%2F&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988"> </li> <li><cite class="citation encyclopaedia">Krips, Henry. <a rel="nofollow" class="external text" href="https://plato.stanford.edu/entries/qt-measurement/">Measurement in Quantum Theory</a>. <a href="/wiki/%E7%88%B1%E5%BE%B7%E5%8D%8E%C2%B7%E6%89%8E%E5%B0%94%E5%A1%94" title="爱德华·扎尔塔">扎尔塔, 爱德华·N</a> (编). 《<a href="/wiki/%E5%8F%B2%E4%B8%B9%E4%BD%9B%E5%93%B2%E5%AD%B8%E7%99%BE%E7%A7%91%E5%85%A8%E6%9B%B8" title="史丹佛哲學百科全書">斯坦福哲学百科全书</a>》.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6&rft.atitle=Measurement+in+Quantum+Theory&rft.aufirst=Henry&rft.aulast=Krips&rft.btitle=%E3%80%8A-%7Bzh-hans%3A%E6%96%AF%E5%9D%A6%E7%A6%8F%3B+zh-tw%3A%E5%8F%B2%E4%B8%B9%E4%BD%9B%3Bzh-mo%3A%E5%8F%B2%E4%B8%B9%E7%A6%8F%3Bzh-hk%3A%E5%8F%B2%E4%B8%B9%E7%A6%8F%7D-%E5%93%B2%E5%AD%A6%E7%99%BE%E7%A7%91%E5%85%A8%E4%B9%A6%E3%80%8B&rft.genre=bookitem&rft_id=https%3A%2F%2Fplato.stanford.edu%2Fentries%2Fqt-measurement%2F&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988"> </li></ul> <div style="clear: both; height: 1em"></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r84265675"><style data-mw-deduplicate="TemplateStyles:r84261037">.mw-parser-output .navbox{box-sizing:border-box;border:1px solid #a2a9b1;width:100%;clear:both;font-size:88%;text-align:center;padding:1px;margin:1em auto 0}.mw-parser-output .navbox .navbox{margin-top:0}.mw-parser-output .navbox+.navbox,.mw-parser-output .navbox+.navbox-styles+.navbox{margin-top:-1px}.mw-parser-output .navbox-inner,.mw-parser-output .navbox-subgroup{width:100%}.mw-parser-output .navbox-group,.mw-parser-output .navbox-title,.mw-parser-output .navbox-abovebelow{text-align:center;padding-left:1em;padding-right:1em}.mw-parser-output .navbox-group{white-space:nowrap;text-align:right}.mw-parser-output .navbox,.mw-parser-output .navbox-subgroup{background-color:#fdfdfd}.mw-parser-output .navbox-list{border-color:#fdfdfd}.mw-parser-output .navbox-list-with-group{text-align:left;border-left-width:2px;border-left-style:solid}.mw-parser-output tr+tr>.navbox-abovebelow,.mw-parser-output tr+tr>.navbox-group,.mw-parser-output tr+tr>.navbox-image,.mw-parser-output tr+tr>.navbox-list{border-top:2px solid #fdfdfd}.mw-parser-output .navbox-title{background-color:#ccf;position:relative}.mw-parser-output .navbox-abovebelow,.mw-parser-output .navbox-group,.mw-parser-output .navbox-subgroup .navbox-title{background-color:#ddf}.mw-parser-output .navbox-subgroup .navbox-group,.mw-parser-output .navbox-subgroup .navbox-abovebelow{background-color:#e6e6ff}.mw-parser-output .navbox-even{background-color:#f7f7f7}.mw-parser-output .navbox-odd{background-color:transparent}.mw-parser-output .navbox .hlist td dl,.mw-parser-output .navbox .hlist td ol,.mw-parser-output .navbox .hlist td ul,.mw-parser-output .navbox td.hlist dl,.mw-parser-output .navbox td.hlist ol,.mw-parser-output .navbox td.hlist ul{padding:0.125em 0}.mw-parser-output .navbox .navbar{display:block;font-size:100%}.mw-parser-output .navbox-title .navbar{float:left;text-align:left;margin-right:0.5em;width:auto;padding-left:0.2em;position:absolute;left:1em}.mw-parser-output .navbox .mw-collapsible-toggle{margin-left:0.5em;position:absolute;right:1em}body.skin--responsive .mw-parser-output .navbox-image img{max-width:none!important}@media print{body.ns-0 .mw-parser-output .navbox{display:none!important}}</style></div><div role="navigation" class="navbox" aria-labelledby="量子力学" style="padding:3px"><table class="nowraplinks hlist mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="collapsible-title navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r84265675"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r84244141"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Quantum_mechanics_topics" title="Template:Quantum mechanics topics"><abbr title="查看该模板">查</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Quantum_mechanics_topics" title="Template talk:Quantum mechanics topics"><abbr title="讨论该模板">论</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:%E7%BC%96%E8%BE%91%E9%A1%B5%E9%9D%A2/Template:Quantum_mechanics_topics" title="Special:编辑页面/Template:Quantum mechanics topics"><abbr title="编辑该模板">编</abbr></a></li></ul></div><div id="量子力学" style="font-size:110%;margin:0 5em"><a class="mw-selflink selflink">量子力学</a></div></th></tr><tr><td class="navbox-abovebelow" colspan="2"><div> <ul><li><a href="/wiki/%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%B8%E5%85%A5%E9%96%80" title="量子力學入門">入門</a></li> <li><a href="/wiki/%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%B8%E7%9A%84%E6%95%B8%E5%AD%B8%E8%A1%A8%E8%BF%B0" title="量子力學的數學表述">數學表述</a></li> <li><a href="/wiki/%E7%89%A9%E7%90%86%E5%AD%A6%E5%8F%B2#量子理论" title="物理学史">歷史</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">背景</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%B8%E5%85%A5%E9%96%80" title="量子力學入門">入門</a></li> <li><a href="/wiki/%E7%89%A9%E7%90%86%E5%AD%A6%E5%8F%B2#量子理论" title="物理学史">歷史</a> <ul><li><a href="/w/index.php?title=%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%B8%E6%99%82%E9%96%93%E8%BB%B8&action=edit&redlink=1" class="new" title="量子力學時間軸（页面不存在）">量子力學時間軸</a>（英语：<a href="https://en.wikipedia.org/wiki/Timeline_of_quantum_mechanics" class="extiw" title="en:Timeline of quantum mechanics">Timeline of quantum mechanics</a>）</li></ul></li> <li><a href="/wiki/%E7%BB%8F%E5%85%B8%E5%8A%9B%E5%AD%A6" title="经典力学">经典力学</a></li> <li><a href="/wiki/%E8%88%8A%E9%87%8F%E5%AD%90%E8%AB%96" title="舊量子論">舊量子論</a></li> <li><a href="/w/index.php?title=%E5%9F%BA%E6%9C%AC%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%B8%E8%A9%9E%E5%BD%99%E8%A1%A8&action=edit&redlink=1" class="new" title="基本量子力學詞彙表（页面不存在）">基本量子力學詞彙表</a>（英语：<a href="https://en.wikipedia.org/wiki/Glossary_of_elementary_quantum_mechanics" class="extiw" title="en:Glossary of elementary quantum mechanics">Glossary of elementary quantum mechanics</a>）</li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">基礎</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E7%8B%84%E6%8B%89%E5%85%8B%E7%AC%A6%E5%8F%B7" title="狄拉克符号">狄拉克符号</a></li> <li><a href="/wiki/%E4%BA%92%E8%A1%A5%E5%8E%9F%E7%90%86" title="互补原理">互补原理</a></li> <li><a href="/wiki/%E5%AF%86%E5%BA%A6%E7%9F%A9%E9%99%A3" title="密度矩陣">密度矩陣</a></li> <li><a href="/wiki/%E8%83%BD%E7%BA%A7" title="能级">能级</a> <ul><li><a href="/wiki/%E5%9F%BA%E6%80%81" title="基态">基态</a></li> <li><a href="/wiki/%E6%BF%80%E5%8F%91%E6%80%81" title="激发态">激发态</a></li> <li><a href="/wiki/%E7%AE%80%E5%B9%B6%E8%83%BD%E7%BA%A7" title="简并能级">简并能级</a></li> <li><a href="/wiki/%E9%9B%B6%E9%BB%9E%E8%83%BD%E9%87%8F" title="零點能量">零點能量</a></li></ul></li> <li><a href="/wiki/%E9%87%8F%E5%AD%90%E7%BA%8F%E7%B5%90" title="量子纏結">量子纏結</a></li> <li><a href="/wiki/%E5%93%88%E5%AF%86%E9%A1%BF%E7%AE%97%E7%AC%A6" title="哈密顿算符">哈密顿算符</a></li> <li><a href="/wiki/%E5%B9%B2%E6%B6%89_(%E7%89%A9%E7%90%86%E5%AD%A6)" title="干涉 (物理学)">干涉</a></li> <li><a href="/wiki/%E9%87%8F%E5%AD%90%E9%80%80%E7%9B%B8%E5%B9%B2" title="量子退相干">量子退相干</a></li> <li><a href="/wiki/%E9%87%8F%E5%AD%90%E6%B8%AC%E9%87%8F" title="量子測量">量子測量</a></li> <li><a href="/w/index.php?title=%E9%87%8F%E5%AD%90%E9%9D%9E%E5%B1%80%E9%83%A8%E6%80%A7&action=edit&redlink=1" class="new" title="量子非局部性（页面不存在）">量子非局部性</a>（英语：<a href="https://en.wikipedia.org/wiki/Quantum_nonlocality" class="extiw" title="en:Quantum nonlocality">Quantum nonlocality</a>）</li> <li><a href="/wiki/%E9%87%8F%E5%AD%90%E6%85%8B" title="量子態">量子態</a></li> <li><a href="/wiki/%E6%80%81%E5%8F%A0%E5%8A%A0%E5%8E%9F%E7%90%86" title="态叠加原理">态叠加原理</a></li> <li><a href="/wiki/%E9%87%8F%E5%AD%90%E7%A9%BF%E9%9A%A7%E6%95%88%E6%87%89" title="量子穿隧效應">量子穿隧效應</a></li> <li><a href="/w/index.php?title=%E6%95%A3%E5%B0%84%E7%90%86%E8%AB%96&action=edit&redlink=1" class="new" title="散射理論（页面不存在）">散射理論</a>（英语：<a href="https://en.wikipedia.org/wiki/Scattering_theory" class="extiw" title="en:Scattering theory">Scattering theory</a>）</li> <li><a href="/w/index.php?title=%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%B8%E5%B0%8D%E7%A8%B1%E6%80%A7&action=edit&redlink=1" class="new" title="量子力學對稱性（页面不存在）">量子力學對稱性</a>（英语：<a href="https://en.wikipedia.org/wiki/Symmetry_in_quantum_mechanics" class="extiw" title="en:Symmetry in quantum mechanics">Symmetry in quantum mechanics</a>）</li> <li><a href="/wiki/%E4%B8%8D%E7%A1%AE%E5%AE%9A%E6%80%A7%E5%8E%9F%E7%90%86" title="不确定性原理">不确定性原理</a></li> <li><a href="/wiki/%E6%B3%A2%E5%87%BD%E6%95%B0" title="波函数">波函数</a> <ul><li><a href="/wiki/%E6%B3%A2%E5%87%BD%E6%95%B0%E5%9D%8D%E7%BC%A9" title="波函数坍缩">波函数坍缩</a></li> <li><a href="/wiki/%E6%B3%A2%E7%B2%92%E4%BA%8C%E8%B1%A1%E6%80%A7" title="波粒二象性">波粒二象性</a></li></ul></li> <li><a href="/w/index.php?title=%E9%87%8F%E5%AD%90%E8%B7%B3%E8%BA%8D&action=edit&redlink=1" class="new" title="量子跳躍（页面不存在）">量子跳躍</a>（英语：<a href="https://en.wikipedia.org/wiki/Atomic_electron_transition" class="extiw" title="en:Atomic electron transition">Atomic electron transition</a>）</li> <li><a href="/wiki/%E9%87%8F%E5%AD%90%E4%BD%8D%E5%85%83" title="量子位元">量子位元</a></li> <li><a href="/wiki/%E9%87%8F%E5%AD%90%E4%B8%89%E4%BD%8D%E5%85%83" title="量子三位元">量子三位元</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">表述</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%B8%E7%9A%84%E6%95%B8%E5%AD%B8%E8%A1%A8%E8%BF%B0" title="量子力學的數學表述">量子力學的數學表述</a></li> <li><a href="/wiki/%E6%B5%B7%E6%A3%AE%E5%A0%A1%E7%B9%AA%E6%99%AF" title="海森堡繪景">海森堡繪景</a></li> <li><a href="/wiki/%E7%9B%B8%E4%BA%92%E4%BD%9C%E7%94%A8%E7%B9%AA%E6%99%AF" title="相互作用繪景">相互作用繪景</a></li> <li><a href="/wiki/%E7%9F%A9%E9%99%A3%E5%8A%9B%E5%AD%B8" title="矩陣力學">矩陣力學</a></li> <li><a href="/wiki/%E8%96%9B%E4%B8%81%E6%A0%BC%E7%B9%AA%E6%99%AF" title="薛丁格繪景">薛丁格繪景</a></li> <li><a href="/wiki/%E8%B7%AF%E5%BE%91%E7%A9%8D%E5%88%86%E8%A1%A8%E8%BF%B0" title="路徑積分表述">路徑積分表述</a></li> <li><a href="/wiki/%E7%9B%B8%E7%A9%BA%E9%97%B4%E8%A1%A8%E8%BF%B0" title="相空间表述">相空间表述</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">方程</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E7%8B%84%E6%8B%89%E5%85%8B%E6%96%B9%E7%A8%8B%E5%BC%8F" title="狄拉克方程式">狄拉克方程式</a></li> <li><a href="/wiki/%E5%85%8B%E8%8E%B1%E5%9B%A0-%E6%88%88%E5%B0%94%E7%99%BB%E6%96%B9%E7%A8%8B" title="克莱因-戈尔登方程">克莱因-戈尔登方程</a></li> <li><a href="/wiki/%E5%8C%85%E7%AB%8B%E6%96%B9%E7%A8%8B%E5%BC%8F" title="包立方程式">包立方程式</a></li> <li><a href="/wiki/%E8%96%9B%E5%AE%9A%E8%B0%94%E6%96%B9%E7%A8%8B" title="薛定谔方程">薛定谔方程</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">空間幾何</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E5%B8%83%E6%B4%9B%E8%B5%AB%E7%90%83%E9%9D%A2" title="布洛赫球面">布洛赫球面</a></li> <li><a href="/w/index.php?title=%E6%97%8B%E7%9F%A2%E7%A9%BA%E9%96%93&action=edit&redlink=1" class="new" title="旋矢空間（页面不存在）">旋矢空間</a>（英语：<a href="https://en.wikipedia.org/wiki/Gyrovector_space" class="extiw" title="en:Gyrovector space">Gyrovector space</a>）</li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">詮釋</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%B8%E8%A9%AE%E9%87%8B" title="量子力學詮釋">量子力學詮釋</a></li> <li><a href="/w/index.php?title=%E9%87%8F%E5%AD%90%E8%B2%9D%E8%91%89%E6%96%AF%E8%A9%AE%E9%87%8B&action=edit&redlink=1" class="new" title="量子貝葉斯詮釋（页面不存在）">量子貝葉斯詮釋</a>（英语：<a href="https://en.wikipedia.org/wiki/Quantum_Bayesianism" class="extiw" title="en:Quantum Bayesianism">Quantum Bayesianism</a>）</li> <li><a href="/wiki/%E4%B8%80%E8%87%B4%E6%80%A7%E5%8E%86%E5%8F%B2" title="一致性历史">一致性历史</a></li> <li><a href="/wiki/%E5%93%A5%E6%9C%AC%E5%93%88%E6%A0%B9%E8%A9%AE%E9%87%8B" title="哥本哈根詮釋">哥本哈根詮釋</a></li> <li><a href="/wiki/%E5%BE%B7%E5%B8%83%E7%BD%97%E6%84%8F-%E7%8E%BB%E5%A7%86%E7%90%86%E8%AE%BA" title="德布罗意-玻姆理论">德布罗意-玻姆理论</a></li> <li><a href="/wiki/%E7%B3%BB%E7%B6%9C%E8%A9%AE%E9%87%8B" title="系綜詮釋">系綜詮釋</a></li> <li><a href="/wiki/%E9%9A%B1%E8%AE%8A%E9%87%8F%E7%90%86%E8%AB%96" title="隱變量理論">隱變量理論</a></li> <li><a href="/wiki/%E5%A4%9A%E4%B8%96%E7%95%8C%E8%AF%A0%E9%87%8A" title="多世界诠释">多世界诠释</a></li> <li><a href="/wiki/%E5%AE%A2%E8%A7%80%E5%9D%8D%E7%B8%AE%E7%90%86%E8%AB%96" title="客觀坍縮理論">客觀坍縮理論</a></li> <li><a href="/w/index.php?title=%E9%87%8F%E5%AD%90%E9%82%8F%E8%BC%AF&action=edit&redlink=1" class="new" title="量子邏輯（页面不存在）">量子邏輯</a>（英语：<a href="https://en.wikipedia.org/wiki/Quantum_logic" class="extiw" title="en:Quantum logic">Quantum logic</a>）</li> <li><a href="/wiki/%E9%97%9C%E4%BF%82%E6%80%A7%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%B8" title="關係性量子力學">關係性量子力學</a></li> <li><a href="/w/index.php?title=%E9%9A%A8%E6%A9%9F%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%B8&action=edit&redlink=1" class="new" title="隨機量子力學（页面不存在）">隨機量子力學</a>（英语：<a href="https://en.wikipedia.org/wiki/Stochastic_quantum_mechanics" class="extiw" title="en:Stochastic quantum mechanics">Stochastic quantum mechanics</a>）</li> <li><a href="/wiki/%E4%BA%A4%E6%98%93%E8%A9%AE%E9%87%8B" title="交易詮釋">交易詮釋</a></li> <li><a href="/wiki/%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6%E7%9A%84%E5%AE%87%E5%AE%99%E5%AD%A6%E8%AF%A0%E9%87%8A" title="量子力学的宇宙学诠释">宇宙学诠释</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">實驗</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E9%98%BF%E5%BC%97%E6%B2%99%E7%88%BE%E5%AF%A6%E9%A9%97" title="阿弗沙爾實驗">阿弗沙爾實驗</a></li> <li><a href="/w/index.php?title=%E8%B2%9D%E7%88%BE%E6%B8%AC%E8%A9%A6%E5%AF%A6%E9%A9%97&action=edit&redlink=1" class="new" title="貝爾測試實驗（页面不存在）">貝爾測試實驗</a>（英语：<a href="https://en.wikipedia.org/wiki/Bell_test_experiments" class="extiw" title="en:Bell test experiments">Bell test experiments</a>）</li> <li><a href="/w/index.php?title=%E5%86%B7%E5%8E%9F%E5%AD%90%E5%AF%A6%E9%A9%97%E5%AE%A4&action=edit&redlink=1" class="new" title="冷原子實驗室（页面不存在）">冷原子實驗室</a>（英语：<a href="https://en.wikipedia.org/wiki/Cold_Atom_Laboratory" class="extiw" title="en:Cold Atom Laboratory">Cold Atom Laboratory</a>）</li> <li><a href="/wiki/%E6%88%B4%E7%B6%AD%E6%A3%AE-%E9%9D%A9%E6%9C%AB%E5%AF%A6%E9%A9%97" title="戴維森-革末實驗">戴維森-革末實驗</a></li> <li><a href="/wiki/%E5%BB%B6%E9%81%B2%E9%81%B8%E6%93%87%E9%87%8F%E5%AD%90%E6%93%A6%E9%99%A4%E5%AF%A6%E9%A9%97" title="延遲選擇量子擦除實驗">延遲選擇量子擦除實驗</a></li> <li><a href="/wiki/%E9%9B%99%E7%B8%AB%E5%AF%A6%E9%A9%97" title="雙縫實驗">雙縫實驗</a></li> <li><a href="/wiki/%E6%B3%95%E8%98%AD%E5%85%8B-%E8%B5%AB%E8%8C%B2%E5%AF%A6%E9%A9%97" title="法蘭克-赫茲實驗">法蘭克-赫茲實驗</a></li> <li><a href="/w/index.php?title=%E8%90%8A%E6%A0%BC%E7%89%B9_-_%E5%8A%A0%E7%88%BE%E6%A0%BC%E4%B8%8D%E7%AD%89%E5%BC%8F&action=edit&redlink=1" class="new" title="萊格特 - 加爾格不等式（页面不存在）">萊格特 - 加爾格不等式</a>（英语：<a href="https://en.wikipedia.org/wiki/Leggett%E2%80%93Garg_inequality" class="extiw" title="en:Leggett–Garg inequality">Leggett–Garg inequality</a>）</li> <li><a href="/wiki/%E9%A6%AC%E8%B5%AB-%E6%9B%BE%E5%BE%B7%E7%88%BE%E5%B9%B2%E6%B6%89%E5%84%80" title="馬赫-曾德爾干涉儀">馬赫-曾德爾干涉儀</a></li> <li><a href="/wiki/%E4%BC%8A%E5%88%A9%E6%BE%A4-%E5%A8%81%E5%BE%B7%E6%9B%BC%E7%82%B8%E5%BD%88%E6%B8%AC%E8%A9%A6%E5%95%8F%E9%A1%8C" title="伊利澤-威德曼炸彈測試問題">伊利澤-威德曼炸彈測試問題</a></li> <li><a href="/wiki/%E6%B3%A2%E6%99%AE%E5%B0%94%E5%AE%9E%E9%AA%8C" title="波普尔实验">波普尔实验</a></li> <li><a href="/wiki/%E9%87%8F%E5%AD%90%E6%93%A6%E9%99%A4%E5%AF%A6%E9%A9%97" title="量子擦除實驗">量子擦除實驗</a></li> <li><a href="/wiki/%E8%96%9B%E5%AE%9A%E8%B0%94%E7%8C%AB" title="薛定谔猫">薛定谔猫</a></li> <li><a href="/wiki/%E6%96%BD%E7%89%B9%E6%81%A9-%E6%A0%BC%E6%8B%89%E8%B5%AB%E5%AE%9E%E9%AA%8C" title="施特恩-格拉赫实验">施特恩-格拉赫实验</a></li> <li><a href="/wiki/%E6%83%A0%E5%8B%92%E5%BB%B6%E8%BF%9F%E9%80%89%E6%8B%A9%E5%AE%9E%E9%AA%8C" title="惠勒延迟选择实验">惠勒延迟选择实验</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/w/index.php?title=%E9%87%8F%E5%AD%90%E5%A5%88%E7%B1%B3%E7%A7%91%E5%AD%B8&action=edit&redlink=1" class="new" title="量子奈米科學（页面不存在）">量子纳米科学</a>（英语：<a href="https://en.wikipedia.org/wiki/Quantum_nanoscience" class="extiw" title="en:Quantum nanoscience">Quantum nanoscience</a>）</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/w/index.php?title=%E9%87%8F%E5%AD%90%E8%B2%9D%E8%91%89%E6%96%AF%E8%A9%AE%E9%87%8B&action=edit&redlink=1" class="new" title="量子貝葉斯詮釋（页面不存在）">量子貝葉斯詮釋</a>（英语：<a href="https://en.wikipedia.org/wiki/Quantum_Bayesianism" class="extiw" title="en:Quantum Bayesianism">Quantum Bayesianism</a>）</li> <li><a href="/wiki/%E9%87%8F%E5%AD%90%E7%94%9F%E7%89%A9%E5%AD%A6" title="量子生物学">量子生物学</a></li> <li><a href="/w/index.php?title=%E9%87%8F%E5%AD%90%E5%BE%AE%E7%A9%8D%E5%88%86&action=edit&redlink=1" class="new" title="量子微積分（页面不存在）">量子微積分</a>（英语：<a href="https://en.wikipedia.org/wiki/Quantum_calculus" class="extiw" title="en:Quantum calculus">Quantum calculus</a>）</li> <li><a href="/wiki/%E9%87%8F%E5%AD%90%E5%8C%96%E5%AD%A6" title="量子化学">量子化学</a></li> <li><a href="/w/index.php?title=%E9%87%8F%E5%AD%90%E6%B7%B7%E6%B2%8C&action=edit&redlink=1" class="new" title="量子混沌（页面不存在）">量子混沌</a>（英语：<a href="https://en.wikipedia.org/wiki/Quantum_chaos" class="extiw" title="en:Quantum chaos">Quantum chaos</a>）</li> <li><a href="/w/index.php?title=%E9%87%8F%E5%AD%90%E8%AA%8D%E7%9F%A5&action=edit&redlink=1" class="new" title="量子認知（页面不存在）">量子認知</a>（英语：<a href="https://en.wikipedia.org/wiki/Quantum_cognition" class="extiw" title="en:Quantum cognition">Quantum cognition</a>）</li> <li><a href="/wiki/%E9%87%8F%E5%AD%90%E5%AE%87%E5%AE%99%E5%AD%B8" title="量子宇宙學">量子宇宙學</a></li> <li><a href="/w/index.php?title=%E9%87%8F%E5%AD%90%E5%BE%AE%E5%88%86&action=edit&redlink=1" class="new" title="量子微分（页面不存在）">量子微分</a>（英语：<a href="https://en.wikipedia.org/wiki/Quantum_differential_calculus" class="extiw" title="en:Quantum differential calculus">Quantum differential calculus</a>）</li> <li><a href="/w/index.php?title=%E9%87%8F%E5%AD%90%E5%8B%95%E5%8A%9B%E5%AD%B8&action=edit&redlink=1" class="new" title="量子動力學（页面不存在）">量子動力學</a>（英语：<a href="https://en.wikipedia.org/wiki/Quantum_dynamics" class="extiw" title="en:Quantum dynamics">Quantum dynamics</a>）</li> <li><a href="/w/index.php?title=%E9%87%8F%E5%AD%90%E6%BC%94%E5%8C%96&action=edit&redlink=1" class="new" title="量子演化（页面不存在）">量子演化</a>（英语：<a href="https://en.wikipedia.org/wiki/Quantum_evolution" class="extiw" title="en:Quantum evolution">Quantum evolution</a>）</li> <li><a href="/w/index.php?title=%E9%87%8F%E5%AD%90%E5%B9%BE%E4%BD%95&action=edit&redlink=1" class="new" title="量子幾何（页面不存在）">量子幾何</a>（英语：<a href="https://en.wikipedia.org/wiki/Quantum_geometry" class="extiw" title="en:Quantum geometry">Quantum geometry</a>）</li> <li><a href="/wiki/%E9%87%8F%E5%AD%90%E7%BE%A4" title="量子群">量子群</a></li> <li><a href="/w/index.php?title=%E6%B8%AC%E9%87%8F%E5%95%8F%E9%A1%8C&action=edit&redlink=1" class="new" title="測量問題（页面不存在）">測量問題</a>（英语：<a href="https://en.wikipedia.org/wiki/Measurement_problem" class="extiw" title="en:Measurement problem">Measurement problem</a>）</li> <li><a href="/w/index.php?title=%E9%87%8F%E5%AD%90%E6%A6%82%E7%8E%87&action=edit&redlink=1" class="new" title="量子概率（页面不存在）">量子概率</a>（英语：<a href="https://en.wikipedia.org/wiki/Quantum_probability" class="extiw" title="en:Quantum probability">Quantum probability</a>）</li> <li><a href="/w/index.php?title=%E9%87%8F%E5%AD%90%E9%9A%A8%E6%A9%9F%E6%BC%94%E7%AE%97&action=edit&redlink=1" class="new" title="量子隨機演算（页面不存在）">量子隨機演算</a>（英语：<a href="https://en.wikipedia.org/wiki/Quantum_stochastic_calculus" class="extiw" title="en:Quantum stochastic calculus">Quantum stochastic calculus</a>）</li> <li><a href="/w/index.php?title=%E9%87%8F%E5%AD%90%E6%99%82%E7%A9%BA&action=edit&redlink=1" class="new" title="量子時空（页面不存在）">量子時空</a>（英语：<a href="https://en.wikipedia.org/wiki/Quantum_spacetime" class="extiw" title="en:Quantum spacetime">Quantum spacetime</a>）</li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/%E9%87%8F%E5%AD%90%E6%8A%80%E8%A1%93" title="量子技術">量子技術</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E9%87%8F%E5%AD%90%E6%BC%94%E7%AE%97%E6%B3%95" title="量子演算法">量子演算法</a></li> <li><a href="/w/index.php?title=%E9%87%8F%E5%AD%90%E6%94%BE%E5%A4%A7%E5%99%A8&action=edit&redlink=1" class="new" title="量子放大器（页面不存在）">量子放大器</a>（英语：<a href="https://en.wikipedia.org/wiki/Quantum_amplifier" class="extiw" title="en:Quantum amplifier">Quantum amplifier</a>）</li> <li><a href="/w/index.php?title=%E9%87%8F%E5%AD%90%E7%B8%BD%E7%B7%9A&action=edit&redlink=1" class="new" title="量子總線（页面不存在）">量子總線</a>（英语：<a href="https://en.wikipedia.org/wiki/Quantum_bus" class="extiw" title="en:Quantum bus">Quantum bus</a>）</li> <li><a href="/wiki/%E9%87%8F%E5%AD%90%E7%82%B9" title="量子点">量子点</a> <ul><li><a href="/w/index.php?title=%E9%87%8F%E5%AD%90%E7%B4%B0%E8%83%9E%E8%87%AA%E5%8B%95%E6%A9%9F&action=edit&redlink=1" class="new" title="量子細胞自動機（页面不存在）">量子細胞自動機</a>（英语：<a href="https://en.wikipedia.org/wiki/Quantum_cellular_automaton" class="extiw" title="en:Quantum cellular automaton">Quantum cellular automaton</a>）</li> <li><a href="/wiki/%E9%87%8F%E5%AD%90%E6%9C%89%E9%99%90%E8%87%AA%E5%8B%95%E6%A9%9F" title="量子有限自動機">量子有限自動機</a></li></ul></li> <li><a href="/w/index.php?title=%E9%87%8F%E5%AD%90%E9%80%9A%E9%81%93&action=edit&redlink=1" class="new" title="量子通道（页面不存在）">量子通道</a>（英语：<a href="https://en.wikipedia.org/wiki/Quantum_channel" class="extiw" title="en:Quantum channel">Quantum channel</a>）</li> <li><a href="/wiki/%E9%87%8F%E5%AD%90%E7%B7%9A%E8%B7%AF" title="量子線路">量子線路</a></li> <li><a href="/wiki/%E9%87%8F%E5%AD%90%E5%A4%8D%E6%9D%82%E6%80%A7%E7%90%86%E8%AE%BA" title="量子复杂性理论">量子复杂性理论</a></li> <li><a href="/wiki/%E9%87%8F%E5%AD%90%E8%AE%A1%E7%AE%97%E6%9C%BA" title="量子计算机">量子计算机</a> <ul><li><a href="/w/index.php?title=%E9%87%8F%E5%AD%90%E8%A8%88%E7%AE%97%E6%99%82%E9%96%93%E8%BB%B8&action=edit&redlink=1" class="new" title="量子計算時間軸（页面不存在）">量子計算時間軸</a>（英语：<a href="https://en.wikipedia.org/wiki/Timeline_of_quantum_computing" class="extiw" title="en:Timeline of quantum computing">Timeline of quantum computing</a>）</li></ul></li> <li><a href="/wiki/%E9%87%8F%E5%AD%90%E5%AF%86%E7%A2%BC%E5%AD%B8" title="量子密碼學">量子密碼學</a></li> <li><a href="/wiki/%E9%87%8F%E5%AD%90%E5%85%89%E5%AD%A6" title="量子光学">量子電子學</a></li> <li><a href="/w/index.php?title=%E9%87%8F%E5%AD%90%E8%AA%A4%E5%B7%AE%E6%A0%A1%E6%AD%A3&action=edit&redlink=1" class="new" title="量子誤差校正（页面不存在）">量子誤差校正</a>（英语：<a href="https://en.wikipedia.org/wiki/Quantum_error_correction" class="extiw" title="en:Quantum error correction">Quantum error correction</a>）</li> <li><a href="/wiki/%E9%87%8F%E5%AD%90%E6%88%90%E5%83%8F" title="量子成像">量子成像</a></li> <li><a href="/w/index.php?title=%E9%87%8F%E5%AD%90%E5%9C%96%E5%83%8F%E8%99%95%E7%90%86&action=edit&redlink=1" class="new" title="量子圖像處理（页面不存在）">量子圖像處理</a>（英语：<a href="https://en.wikipedia.org/wiki/Quantum_image_processing" class="extiw" title="en:Quantum image processing">Quantum image processing</a>）</li> <li><a href="/wiki/%E9%87%8F%E5%AD%90%E4%BF%A1%E6%81%AF" title="量子信息">量子信息</a></li> <li><a href="/wiki/%E9%87%8F%E5%AD%90%E5%AF%86%E9%91%B0%E5%88%86%E7%99%BC" title="量子密鑰分發">量子密鑰分發</a></li> <li><a href="/w/index.php?title=%E9%87%8F%E5%AD%90%E9%82%8F%E8%BC%AF&action=edit&redlink=1" class="new" title="量子邏輯（页面不存在）">量子邏輯</a>（英语：<a href="https://en.wikipedia.org/wiki/Quantum_logic" class="extiw" title="en:Quantum logic">Quantum logic</a>）</li> <li><a href="/wiki/%E9%87%8F%E5%AD%90%E9%96%98" title="量子閘">量子閘</a></li> <li><a href="/w/index.php?title=%E9%87%8F%E5%AD%90%E6%A9%9F&action=edit&redlink=1" class="new" title="量子機（页面不存在）">量子機</a>（英语：<a href="https://en.wikipedia.org/wiki/Quantum_machine" class="extiw" title="en:Quantum machine">Quantum machine</a>）</li> <li><a href="/wiki/%E9%87%8F%E5%AD%90%E6%A9%9F%E5%99%A8%E5%AD%B8%E7%BF%92" title="量子機器學習">量子機器學習</a></li> <li><a href="/w/index.php?title=%E9%87%8F%E5%AD%90%E8%B6%85%E6%9D%90%E6%96%99&action=edit&redlink=1" class="new" title="量子超材料（页面不存在）">量子超材料</a>（英语：<a href="https://en.wikipedia.org/wiki/Quantum_metamaterial" class="extiw" title="en:Quantum metamaterial">Quantum metamaterial</a>）</li> <li><a href="/w/index.php?title=%E9%87%8F%E5%AD%90%E8%A8%88%E9%87%8F%E5%AD%B8&action=edit&redlink=1" class="new" title="量子計量學（页面不存在）">量子計量學</a>（英语：<a href="https://en.wikipedia.org/wiki/Quantum_metrology" class="extiw" title="en:Quantum metrology">Quantum metrology</a>）</li> <li><a href="/w/index.php?title=%E9%87%8F%E5%AD%90%E7%BD%91%E7%BB%9C&action=edit&redlink=1" class="new" title="量子网络（页面不存在）">量子网络</a>（英语：<a href="https://en.wikipedia.org/wiki/Quantum_network" class="extiw" title="en:Quantum network">Quantum network</a>）</li> <li><a href="/w/index.php?title=%E9%87%8F%E5%AD%90%E7%A5%9E%E7%B6%93%E7%B6%B2%E7%B5%A1&action=edit&redlink=1" class="new" title="量子神經網絡（页面不存在）">量子神經網絡</a>（英语：<a href="https://en.wikipedia.org/wiki/Quantum_neural_network" class="extiw" title="en:Quantum neural network">Quantum neural network</a>）</li> <li><a href="/wiki/%E9%87%8F%E5%AD%90%E5%85%89%E5%AD%A6" title="量子光学">量子光学</a></li> <li><a href="/wiki/%E9%87%8F%E5%AD%90%E7%B7%A8%E7%A8%8B" title="量子編程">量子編程</a></li> <li><a href="/w/index.php?title=%E9%87%8F%E5%AD%90%E5%82%B3%E6%84%9F%E5%99%A8&action=edit&redlink=1" class="new" title="量子傳感器（页面不存在）">量子傳感器</a>（英语：<a href="https://en.wikipedia.org/wiki/Quantum_sensor" class="extiw" title="en:Quantum sensor">Quantum sensor</a>）</li> <li><a href="/w/index.php?title=%E9%87%8F%E5%AD%90%E6%A8%A1%E6%93%AC%E5%99%A8&action=edit&redlink=1" class="new" title="量子模擬器（页面不存在）">量子模擬器</a>（英语：<a href="https://en.wikipedia.org/wiki/Quantum_simulator" class="extiw" title="en:Quantum simulator">Quantum simulator</a>）</li> <li><a href="/wiki/%E9%87%8F%E5%AD%90%E9%9A%B1%E5%BD%A2%E5%82%B3%E6%85%8B" title="量子隱形傳態">量子隱形傳態</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">進階研究</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E9%87%8F%E5%AD%90%E7%BB%9F%E8%AE%A1%E5%8A%9B%E5%AD%A6" title="量子统计力学">量子統計力學</a>（英语：<a href="https://en.wikipedia.org/wiki/Quantum_statistical_mechanics" class="extiw" title="en:Quantum statistical mechanics">Quantum statistical mechanics</a>）</li> <li><a href="/w/index.php?title=%E7%9B%B8%E5%B0%8D%E8%AB%96%E4%B9%8B%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%B8&action=edit&redlink=1" class="new" title="相對論之量子力學（页面不存在）">相對論之量子力學</a>（英语：<a href="https://en.wikipedia.org/wiki/Relativistic_quantum_mechanics" class="extiw" title="en:Relativistic quantum mechanics">Relativistic quantum mechanics</a>）</li> <li><a href="/wiki/%E9%87%8F%E5%AD%90%E5%9C%BA%E8%AE%BA" title="量子场论">量子场论</a> <ul><li><a href="/w/index.php?title=%E9%87%8F%E5%AD%90%E5%A0%B4%E7%90%86%E8%AB%96%E5%8F%B2&action=edit&redlink=1" class="new" title="量子場理論史（页面不存在）">量子場理論史</a>（英语：<a href="https://en.wikipedia.org/wiki/History_of_quantum_field_theory" class="extiw" title="en:History of quantum field theory">History of quantum field theory</a>）</li></ul></li> <li><a href="/wiki/%E9%87%8F%E5%AD%90%E5%BC%95%E5%8A%9B" title="量子引力">量子引力</a></li> <li><a href="/w/index.php?title=%E5%88%86%E6%95%B8%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%B8&action=edit&redlink=1" class="new" title="分數量子力學（页面不存在）">分數量子力學</a>（英语：<a href="https://en.wikipedia.org/wiki/Fractional_quantum_mechanics" class="extiw" title="en:Fractional quantum mechanics">Fractional quantum mechanics</a>）</li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">物理學者</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E9%A9%AC%E5%85%8B%E6%96%AF%C2%B7%E6%99%AE%E6%9C%97%E5%85%8B" title="马克斯·普朗克">普朗克</a></li> <li><a href="/wiki/%E5%B0%BC%E5%B0%94%E6%96%AF%C2%B7%E7%8E%BB%E5%B0%94" title="尼尔斯·玻尔">玻尔</a></li> <li><a href="/wiki/%E4%BF%9D%E7%BD%97%C2%B7%E5%9F%83%E4%BC%A6%E8%B4%B9%E6%96%AF%E7%89%B9" title="保罗·埃伦费斯特">埃倫費斯特</a></li> <li><a href="/wiki/%E7%BB%B4%E5%B0%94%E7%BA%B3%C2%B7%E6%B5%B7%E6%A3%AE%E5%A0%A1" title="维尔纳·海森堡">海森堡</a></li> <li><a href="/wiki/%E5%9F%83%E5%B0%94%E6%B8%A9%C2%B7%E8%96%9B%E5%AE%9A%E8%B0%94" title="埃尔温·薛定谔">薛丁格</a></li> <li><a href="/wiki/%E8%B7%AF%E6%98%93%C2%B7%E5%BE%B7%E5%B8%83%E7%BD%97%E6%84%8F" title="路易·德布罗意">德布羅意</a></li> <li><a href="/wiki/%E9%A9%AC%E5%85%8B%E6%96%AF%C2%B7%E7%8E%BB%E6%81%A9" title="马克斯·玻恩">玻恩</a></li> <li><a href="/wiki/%E9%98%BF%E5%B0%94%E4%BC%AF%E7%89%B9%C2%B7%E7%88%B1%E5%9B%A0%E6%96%AF%E5%9D%A6" title="阿尔伯特·爱因斯坦">愛因斯坦</a></li> <li><a href="/wiki/%E4%BC%91%C2%B7%E8%89%BE%E5%BC%97%E9%9B%B7%E7%89%B9%E4%B8%89%E4%B8%96" title="休·艾弗雷特三世">艾弗雷特</a></li> <li><a href="/wiki/%E9%98%BF%E8%AB%BE%C2%B7%E7%B4%A2%E6%9C%AB%E8%8F%B2" title="阿諾·索末菲">索末菲</a></li> <li><a href="/wiki/%E7%BA%A6%E7%BF%B0%C2%B7%E5%86%AF%E8%AF%BA%E4%BC%8A%E6%9B%BC" title="约翰·冯诺伊曼">馮诺伊曼</a></li> <li><a href="/wiki/%E7%90%86%E6%9F%A5%E5%BE%B7%C2%B7%E8%B2%BB%E6%9B%BC" title="理查德·費曼">費曼</a></li> <li><a href="/wiki/%E4%BF%9D%E7%BD%97%C2%B7%E7%8B%84%E6%8B%89%E5%85%8B" title="保罗·狄拉克">狄拉克</a></li> <li><a href="/wiki/%E6%B2%83%E5%B0%94%E5%A4%AB%E5%86%88%C2%B7%E6%B3%A1%E5%88%A9" title="沃尔夫冈·泡利">泡利</a></li> <li><a href="/wiki/%E5%A8%81%E5%BB%89%C2%B7%E7%BB%B4%E6%81%A9" title="威廉·维恩">維恩</a></li> <li><a href="/wiki/%E6%88%B4%E7%BB%B4%C2%B7%E7%8E%BB%E5%A7%86" title="戴维·玻姆">玻姆</a></li> <li><a href="/wiki/%E7%B4%84%E7%BF%B0%C2%B7%E8%B2%9D%E7%88%BE" class="mw-disambig" title="約翰·貝爾">貝爾</a></li> <li><a href="/wiki/%E5%AE%89%E4%B8%9C%C2%B7%E8%94%A1%E6%9E%97%E6%A0%BC" title="安东·蔡林格">蔡林格</a></li></ul> </div></td></tr><tr><td class="navbox-abovebelow" colspan="2"><div> <ul><li><img alt="分类" src="//upload.wikimedia.org/wikipedia/commons/thumb/9/96/Symbol_category_class.svg/16px-Symbol_category_class.svg.png" decoding="async" width="16" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/96/Symbol_category_class.svg/23px-Symbol_category_class.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/96/Symbol_category_class.svg/31px-Symbol_category_class.svg.png 2x" data-file-width="180" data-file-height="185" /> <a href="/wiki/Category:%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6" title="Category:量子力学">分类</a></li> <li><img alt="主题" src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e2/Symbol_portal_class.svg/16px-Symbol_portal_class.svg.png" decoding="async" width="16" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e2/Symbol_portal_class.svg/23px-Symbol_portal_class.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e2/Symbol_portal_class.svg/31px-Symbol_portal_class.svg.png 2x" data-file-width="180" data-file-height="185" /> <a href="/wiki/Portal:%E7%89%A9%E7%90%86%E5%AD%A6" title="Portal:物理学">物理学主题</a></li> <li><img alt="共享资源页面" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/12px-Commons-logo.svg.png" decoding="async" width="12" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/18px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/24px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /> <a href="https://commons.wikimedia.org/wiki/Category:Quantum_mechanics" class="extiw" title="commons:Category:Quantum mechanics">维基共享</a></li></ul> </div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r84265675"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r84261037"></div><div role="navigation" class="navbox" aria-labelledby="物理学分支" style="padding:3px"><table class="nowraplinks hlist mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="collapsible-title navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r84265675"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r84244141"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:%E7%89%A9%E7%90%86%E5%AD%B8%E5%88%86%E6%94%AF" title="Template:物理學分支"><abbr title="查看该模板">查</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:%E7%89%A9%E7%90%86%E5%AD%B8%E5%88%86%E6%94%AF" title="Template talk:物理學分支"><abbr title="讨论该模板">论</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:%E7%BC%96%E8%BE%91%E9%A1%B5%E9%9D%A2/Template:%E7%89%A9%E7%90%86%E5%AD%B8%E5%88%86%E6%94%AF" title="Special:编辑页面/Template:物理學分支"><abbr title="编辑该模板">编</abbr></a></li></ul></div><div id="物理学分支" style="font-size:110%;margin:0 5em"><a href="/wiki/%E7%89%A9%E7%90%86%E5%AD%A6" title="物理学">物理学</a><a href="/wiki/Category:%E7%89%A9%E7%90%86%E5%AD%A6%E5%88%86%E6%94%AF" title="Category:物理学分支">分支</a></div></th></tr><tr><td class="navbox-abovebelow" colspan="2"><div><a href="/wiki/%E7%89%A9%E7%90%86%E5%AD%A6%E5%8F%B2" title="物理学史">物理学史</a></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">组成部分</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E7%90%86%E8%AE%BA%E7%89%A9%E7%90%86%E5%AD%A6" title="理论物理学">理论物理</a></li> <li><a href="/wiki/%E5%AF%A6%E9%A9%97%E7%89%A9%E7%90%86%E5%AD%B8" title="實驗物理學">实验物理</a></li> <li><a href="/wiki/%E5%BA%94%E7%94%A8%E7%89%A9%E7%90%86%E5%AD%A6" title="应用物理学">应用物理</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/%E8%83%BD%E9%87%8F" title="能量">能量</a> · <a href="/wiki/%E9%81%8B%E5%8B%95_(%E7%89%A9%E7%90%86%E5%AD%B8)" title="運動 (物理學)">运动</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E7%83%AD%E5%8A%9B%E5%AD%A6" title="热力学">热力学</a></li> <li><a href="/wiki/%E5%8A%9B%E5%AD%A6" title="力学">力学</a> <ul><li><a href="/wiki/%E7%BB%8F%E5%85%B8%E5%8A%9B%E5%AD%A6" title="经典力学">经典力学</a> <ul><li><a href="/wiki/%E5%BC%B9%E9%81%93%E5%AD%A6" title="弹道学">弹道</a></li> <li><a href="/wiki/%E6%8B%89%E6%A0%BC%E6%9C%97%E6%97%A5%E5%8A%9B%E5%AD%A6" title="拉格朗日力学">拉格朗日</a></li> <li><a href="/wiki/%E5%93%88%E5%AF%86%E9%A1%BF%E5%8A%9B%E5%AD%A6" title="哈密顿力学">哈密顿</a></li></ul></li> <li><a href="/wiki/%E8%BF%9E%E7%BB%AD%E4%BB%8B%E8%B4%A8%E5%8A%9B%E5%AD%A6" title="连续介质力学">连续介质</a></li> <li><a href="/wiki/%E5%A4%A9%E9%AB%94%E5%8A%9B%E5%AD%B8" title="天體力學">天体</a></li> <li><a href="/wiki/%E7%BB%9F%E8%AE%A1%E5%8A%9B%E5%AD%A6" title="统计力学">统计</a></li> <li><a href="/wiki/%E6%B5%81%E4%BD%93%E5%8A%9B%E5%AD%A6" title="流体力学">流体</a></li> <li><a class="mw-selflink selflink">量子</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/%E6%B3%A2" title="波">波</a> · <a href="/wiki/%E5%9C%BA_(%E7%89%A9%E7%90%86)" title="场 (物理)">场</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E5%BC%95%E5%8A%9B" title="引力">引力</a></li> <li><a href="/wiki/%E7%94%B5%E7%A3%81%E5%AD%A6" title="电磁学">电磁学</a> <ul><li><a href="/wiki/%E7%BB%8F%E5%85%B8%E7%94%B5%E7%A3%81%E5%AD%A6" title="经典电磁学">经典</a></li></ul></li> <li><a href="/wiki/%E9%87%8F%E5%AD%90%E5%9C%BA%E8%AE%BA" title="量子场论">量子场论</a></li> <li><a href="/wiki/%E7%9B%B8%E5%AF%B9%E8%AE%BA" title="相对论">相对论</a> <ul><li><a href="/wiki/%E7%8B%AD%E4%B9%89%E7%9B%B8%E5%AF%B9%E8%AE%BA" title="狭义相对论">狭义相对论</a></li> <li><a href="/wiki/%E5%BB%A3%E7%BE%A9%E7%9B%B8%E5%B0%8D%E8%AB%96" title="廣義相對論">廣義相對論</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">按专业</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E6%95%B8%E7%A2%BC%E7%89%A9%E7%90%86%E5%AD%B8" title="數碼物理學">數碼物理學</a></li> <li><a href="/wiki/%E8%AE%A1%E7%AE%97%E7%89%A9%E7%90%86%E5%AD%A6" title="计算物理学">计算物理学</a></li> <li><a href="/wiki/%E7%B2%92%E5%AD%90%E7%89%A9%E7%90%86%E5%AD%B8" title="粒子物理學">粒子物理學</a></li> <li><a href="/wiki/%E5%8E%9F%E5%AD%90%E6%A0%B8%E7%89%A9%E7%90%86%E5%AD%A6" title="原子核物理学">原子核物理学</a></li> <li><a href="/wiki/%E5%8E%9F%E5%AD%90%E5%88%86%E5%AD%90%E4%B8%8E%E5%85%89%E7%89%A9%E7%90%86%E5%AD%A6" title="原子分子与光物理学">原子分子與光物理學</a> <ul><li><a href="/wiki/%E5%88%86%E5%AD%90%E7%89%A9%E7%90%86%E5%AD%A6" title="分子物理学">分子</a></li> <li><a href="/wiki/%E5%8E%9F%E5%AD%90%E7%89%A9%E7%90%86%E5%AD%A6" title="原子物理学">原子</a></li></ul></li> <li><a href="/wiki/%E7%AD%89%E7%A6%BB%E5%AD%90%E4%BD%93%E7%89%A9%E7%90%86%E5%AD%A6" title="等离子体物理学">等离子体</a></li> <li><a href="/wiki/%E7%BB%9F%E8%AE%A1%E5%8A%9B%E5%AD%A6" title="统计力学">统计</a></li> <li><a href="/wiki/%E5%87%9D%E8%81%9A%E6%80%81%E7%89%A9%E7%90%86%E5%AD%A6" title="凝聚态物理学">凝聚态物理学</a> <ul><li><a href="/wiki/%E5%9B%BA%E4%BD%93%E7%89%A9%E7%90%86%E5%AD%A6" title="固体物理学">固体</a></li> <li><a href="/wiki/%E4%BB%8B%E8%A7%82%E7%89%A9%E7%90%86%E5%AD%A6" title="介观物理学">介观</a></li> <li><a href="/wiki/%E8%BD%AF%E7%89%A9%E8%B4%A8" title="软物质">软</a></li> <li><a href="/wiki/%E9%AB%98%E5%88%86%E5%AD%90%E7%89%A9%E7%90%86%E5%AD%A6" title="高分子物理学">高分子</a></li></ul></li> <li><a href="/wiki/%E5%A3%B0%E5%AD%A6" title="声学">声学</a></li> <li><a href="/wiki/%E5%85%89%E5%AD%A6" title="光学">光学</a> <ul><li><a href="/wiki/%E5%87%A0%E4%BD%95%E5%85%89%E5%AD%A6" title="几何光学">几何</a></li> <li><a href="/wiki/%E7%89%A9%E7%90%86%E5%85%89%E5%AD%A6" title="物理光学">物理</a></li> <li><a href="/wiki/%E9%9D%9E%E7%BA%BF%E6%80%A7%E5%85%89%E5%AD%A6" title="非线性光学">非线性</a></li> <li><a href="/wiki/%E9%87%8F%E5%AD%90%E5%85%89%E5%AD%A6" title="量子光学">量子</a></li></ul></li> <li><a href="/wiki/%E5%A4%A9%E4%BD%93%E7%89%A9%E7%90%86%E5%AD%A6" title="天体物理学">天体物理学</a> <ul><li><a href="/wiki/%E6%A0%B8%E5%A4%A9%E4%BD%93%E7%89%A9%E7%90%86%E5%AD%A6" title="核天体物理学">核</a></li> <li><a href="/wiki/%E6%81%92%E6%98%9F%E7%89%A9%E7%90%86%E5%AD%A6" title="恒星物理学">恒星</a></li> <li><a href="/wiki/%E5%A4%A9%E4%BD%93%E7%B2%92%E5%AD%90%E7%89%A9%E7%90%86%E5%AD%A6" title="天体粒子物理学">天体粒子</a></li> <li><a href="/wiki/%E5%A4%AA%E9%98%B3%E7%89%A9%E7%90%86%E5%AD%A6" title="太阳物理学">太阳</a></li> <li><a href="/wiki/%E7%A9%BA%E9%97%B4%E7%89%A9%E7%90%86%E5%AD%A6" title="空间物理学">空间</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">生命科学中的物理学</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E7%94%9F%E7%89%A9%E7%89%A9%E7%90%86%E5%AD%A6" title="生物物理学">生物物理学</a> <ul><li><a href="/wiki/%E7%94%9F%E7%89%A9%E5%8A%9B%E5%AD%A6" title="生物力学">生物力学</a></li> <li><a href="/wiki/%E5%86%9C%E4%B8%9A%E7%89%A9%E7%90%86%E5%AD%A6" title="农业物理学">农业物理学</a></li></ul></li> <li><a href="/wiki/%E9%86%AB%E5%AD%B8%E7%89%A9%E7%90%86" title="醫學物理">醫學物理</a> <ul><li><a href="/w/index.php?title=%E6%BF%80%E5%85%89%E5%8C%BB%E5%AD%A6&action=edit&redlink=1" class="new" title="激光医学（页面不存在）">激光医学</a>（英语：<a href="https://en.wikipedia.org/wiki/Laser_medicine" class="extiw" title="en:Laser medicine">Laser medicine</a>）</li> <li><a href="/wiki/%E6%A0%B8%E5%8C%BB%E5%AD%A6" title="核医学">核医学</a></li> <li><a href="/wiki/%E9%86%AB%E5%AD%B8%E5%BD%B1%E5%83%8F" title="醫學影像">醫學影像</a></li> <li><a href="/wiki/%E5%BF%83%E7%90%86%E7%89%A9%E7%90%86%E5%AD%A6" title="心理物理学">心理物理学</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/%E7%A7%91%E9%99%85%E6%95%B4%E5%90%88" title="科际整合">交叉学科</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E5%A4%A9%E4%BD%93%E7%89%A9%E7%90%86%E5%AD%A6" title="天体物理学">天体物理学</a></li> <li><a href="/wiki/%E6%95%B0%E5%AD%A6%E7%89%A9%E7%90%86" title="数学物理">数学物理</a></li> <li><a href="/wiki/%E9%9D%9E%E7%BA%BF%E6%80%A7%E7%89%A9%E7%90%86%E5%AD%A6" title="非线性物理学">非线性物理学</a></li> <li><a href="/wiki/%E7%B6%93%E6%BF%9F%E7%89%A9%E7%90%86%E5%AD%B8" title="經濟物理學">经济物理学</a></li> <li><a href="/wiki/%E6%9D%90%E6%96%99%E7%A7%91%E5%AD%A6" title="材料科学">材料科学</a> <ul><li><a href="/wiki/%E9%AB%98%E5%88%86%E5%AD%90%E7%89%A9%E7%90%86%E5%AD%A6" title="高分子物理学">高分子</a></li></ul></li> <li><a href="/wiki/%E7%89%A9%E7%90%86%E5%8C%96%E5%AD%A6" title="物理化学">物理化学</a> / <a href="/wiki/%E5%8C%96%E5%AD%A6%E7%89%A9%E7%90%86%E5%AD%A6" title="化学物理学">化学物理学</a></li> <li><a href="/wiki/%E7%89%A9%E7%90%86%E5%AE%87%E5%AE%99%E5%AD%A6" title="物理宇宙学">物理宇宙学</a></li> <li><a href="/wiki/%E5%A4%A7%E6%B0%94%E7%89%A9%E7%90%86%E5%AD%A6" title="大气物理学">大气</a> <ul><li><a href="/wiki/%E4%BA%91%E7%89%A9%E7%90%86%E5%AD%A6" title="云物理学">云</a></li></ul></li> <li><a href="/wiki/%E5%9C%B0%E7%90%83%E7%89%A9%E7%90%86%E5%AD%A6" title="地球物理学">地球物理学</a></li> <li><a href="/wiki/%E5%9C%9F%E5%A3%A4%E7%89%A9%E7%90%86%E5%AD%B8" title="土壤物理學">土壤物理學</a></li> <li><a href="/wiki/%E7%89%A9%E7%90%86%E6%B5%B7%E6%B4%8B%E5%AD%A6" title="物理海洋学">物理海洋学</a></li> <li><a href="/wiki/%E9%87%8F%E5%AD%90%E4%BF%A1%E6%81%AF%E7%A7%91%E5%AD%A6" title="量子信息科学">量子信息科学</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">有关</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E8%AF%BA%E8%B4%9D%E5%B0%94%E7%89%A9%E7%90%86%E5%AD%A6%E5%A5%96" title="诺贝尔物理学奖">诺贝尔物理学奖</a></li> <li><a href="/wiki/%E7%89%A9%E7%90%86%E6%95%99%E8%82%B2" title="物理教育">物理教育</a></li></ul> </div></td></tr><tr><td class="navbox-abovebelow" colspan="2"><div> <ul><li><img alt="分类" src="//upload.wikimedia.org/wikipedia/commons/thumb/9/96/Symbol_category_class.svg/16px-Symbol_category_class.svg.png" decoding="async" width="16" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/96/Symbol_category_class.svg/23px-Symbol_category_class.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/96/Symbol_category_class.svg/31px-Symbol_category_class.svg.png 2x" data-file-width="180" data-file-height="185" /> <a href="/wiki/Category:%E7%89%A9%E7%90%86%E5%AD%A6" title="Category:物理学">分类</a></li> <li><img alt="主题" src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e2/Symbol_portal_class.svg/16px-Symbol_portal_class.svg.png" decoding="async" width="16" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e2/Symbol_portal_class.svg/23px-Symbol_portal_class.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e2/Symbol_portal_class.svg/31px-Symbol_portal_class.svg.png 2x" data-file-width="180" data-file-height="185" /> <a href="/wiki/Portal:%E7%89%A9%E7%90%86%E5%AD%A6" title="Portal:物理学">主題</a></li> <li><img alt="共享资源页面" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/12px-Commons-logo.svg.png" decoding="async" width="12" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/18px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/24px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /> <a href="https://commons.wikimedia.org/wiki/Category:Physics" class="extiw" title="commons:Category:Physics">共享资源</a></li> <li><img alt="专题" src="//upload.wikimedia.org/wikipedia/commons/thumb/3/37/People_icon.svg/16px-People_icon.svg.png" decoding="async" width="16" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/37/People_icon.svg/24px-People_icon.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/37/People_icon.svg/32px-People_icon.svg.png 2x" data-file-width="100" data-file-height="100" /> <a href="/wiki/WikiProject:%E7%89%A9%E7%90%86%E5%AD%A6" title="WikiProject:物理学">专题</a></li></ul> </div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r84265675"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r84261037"><style data-mw-deduplicate="TemplateStyles:r79005747">.mw-parser-output .tooltip-dotted{border-bottom:1px dotted;cursor:help}</style><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r79005747"></div><div role="navigation" class="navbox authority-control" aria-labelledby="-&#123;zh-cn:规范控制;zh-tw:權威控制;&#125;--&#123;zh-cn:数据库;zh-tw:資料庫&#125;-_frameless&#124;text-top&#124;10px&#124;alt=編輯維基數據鏈接&#124;link=https&#58;//www.wikidata.org/wiki/Q944#identifiers&#124;class=noprint&#124;編輯維基數據鏈接" style="padding:3px"><table class="nowraplinks hlist mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="collapsible-title navbox-title" colspan="2"><div id="-&#123;zh-cn:规范控制;zh-tw:權威控制;&#125;--&#123;zh-cn:数据库;zh-tw:資料庫&#125;-_frameless&#124;text-top&#124;10px&#124;alt=編輯維基數據鏈接&#124;link=https&#58;//www.wikidata.org/wiki/Q944#identifiers&#124;class=noprint&#124;編輯維基數據鏈接" style="font-size:110%;margin:0 5em"><a href="/wiki/Help:%E8%A7%84%E8%8C%83%E6%8E%A7%E5%88%B6" title="Help:规范控制">规范控制数据库</a> <a href="https://www.wikidata.org/wiki/Q944#identifiers" title="編輯維基數據鏈接"><img alt="編輯維基數據鏈接" src="//upload.wikimedia.org/wikipedia/commons/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/10px-OOjs_UI_icon_edit-ltr-progressive.svg.png" decoding="async" width="10" height="10" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/15px-OOjs_UI_icon_edit-ltr-progressive.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/20px-OOjs_UI_icon_edit-ltr-progressive.svg.png 2x" data-file-width="20" data-file-height="20" /></a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">国际</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a rel="nofollow" class="external text" href="http://id.worldcat.org/fast/1085128/">FAST</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">各地</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a rel="nofollow" class="external text" href="http://catalogo.bne.es/uhtbin/authoritybrowse.cgi?action=display&authority_id=XX4576425">西班牙</a></li> <li><a rel="nofollow" class="external text" href="https://catalogue.bnf.fr/ark:/12148/cb11938463d">法国</a></li> <li><a rel="nofollow" class="external text" href="https://data.bnf.fr/ark:/12148/cb11938463d">BnF data</a></li> <li><a rel="nofollow" class="external text" href="https://d-nb.info/gnd/4047989-4">德国</a></li> <li><a rel="nofollow" class="external text" href="http://olduli.nli.org.il/F/?func=find-b&local_base=NLX10&find_code=UID&request=987007550893405171">以色列</a></li> <li><a rel="nofollow" class="external text" href="https://id.loc.gov/authorities/sh85109469">美国</a></li> <li><a rel="nofollow" class="external text" href="https://id.ndl.go.jp/auth/ndlna/00569870">日本</a></li> <li><a rel="nofollow" class="external text" href="https://aleph.nkp.cz/F/?func=find-c&local_base=aut&ccl_term=ica=ph115047&CON_LNG=ENG">捷克</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">其他</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a rel="nofollow" class="external text" href="https://www.idref.fr/02731569X">IdRef</a></li></ul> </div></td></tr></tbody></table></div>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">检索自“<a dir="ltr" href="https://zh.wikipedia.org/w/index.php?title=量子力学&oldid=84856400">https://zh.wikipedia.org/w/index.php?title=量子力学&oldid=84856400</a>”</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Special:%E9%A1%B5%E9%9D%A2%E5%88%86%E7%B1%BB" title="Special:页面分类">分类</a>：<ul><li><a href="/wiki/Category:%E7%89%A9%E7%90%86%E5%AD%B8%E4%B8%AD%E6%9C%AA%E8%A7%A3%E6%B1%BA%E7%9A%84%E5%95%8F%E9%A1%8C" title="Category:物理學中未解決的問題">物理學中未解決的問題</a></li><li><a href="/wiki/Category:%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6" title="Category:量子力学">量子力学</a></li></ul></div><div id="mw-hidden-catlinks" class="mw-hidden-catlinks mw-hidden-cats-hidden">隐藏分类：<ul><li><a href="/wiki/Category:%E5%90%AB%E6%9C%89%E8%BF%87%E6%97%B6%E5%8F%82%E6%95%B0%E7%9A%84%E5%BC%95%E7%94%A8%E7%9A%84%E9%A1%B5%E9%9D%A2" title="Category:含有过时参数的引用的页面">含有过时参数的引用的页面</a></li><li><a href="/wiki/Category:%E5%BC%95%E6%96%87%E6%A0%BC%E5%BC%8F1%E7%BB%B4%E6%8A%A4%EF%BC%9A%E5%86%97%E4%BD%99%E6%96%87%E6%9C%AC" title="Category:引文格式1维护：冗余文本">引文格式1维护：冗余文本</a></li><li><a href="/wiki/Category:%E5%90%AB%E6%9C%89%E8%AE%BF%E9%97%AE%E6%97%A5%E6%9C%9F%E4%BD%86%E6%97%A0%E7%BD%91%E5%9D%80%E7%9A%84%E5%BC%95%E7%94%A8%E7%9A%84%E9%A1%B5%E9%9D%A2" title="Category:含有访问日期但无网址的引用的页面">含有访问日期但无网址的引用的页面</a></li><li><a href="/wiki/Category:%E5%BC%95%E6%96%87%E6%A0%BC%E5%BC%8F1%E7%BB%B4%E6%8A%A4%EF%BC%9A%E6%98%BE%E5%BC%8F%E4%BD%BF%E7%94%A8%E7%AD%89%E6%A0%87%E7%AD%BE" title="Category:引文格式1维护：显式使用等标签">引文格式1维护：显式使用等标签</a></li><li><a href="/wiki/Category:%E5%BC%95%E6%96%87%E6%A0%BC%E5%BC%8F1%E9%94%99%E8%AF%AF%EF%BC%9A%E6%97%A5%E6%9C%9F" title="Category:引文格式1错误：日期">引文格式1错误：日期</a></li><li><a href="/wiki/Category:%E6%9C%89%E5%8D%95%E7%8B%AC%E5%85%A5%E9%97%A8%E4%BB%8B%E7%BB%8D%E7%9A%84%E6%9D%A1%E7%9B%AE" title="Category:有单独入门介绍的条目">有单独入门介绍的条目</a></li><li><a href="/wiki/Category:%E5%84%AA%E8%89%AF%E6%A2%9D%E7%9B%AE" title="Category:優良條目">優良條目</a></li><li><a href="/wiki/Category:%E5%90%AB%E6%9C%89%E8%8B%B1%E8%AA%9E%E7%9A%84%E6%A2%9D%E7%9B%AE" title="Category:含有英語的條目">含有英語的條目</a></li><li><a href="/wiki/Category:%E9%9C%80%E8%A6%81%E6%9F%A5%E8%AD%89%E4%BE%86%E6%BA%90%E7%9A%84%E7%B6%AD%E5%9F%BA%E7%99%BE%E7%A7%91%E6%A2%9D%E7%9B%AE" title="Category:需要查證來源的維基百科條目">需要查證來源的維基百科條目</a></li><li><a href="/wiki/Category:%E4%BD%BF%E7%94%A8%E7%9A%84%E5%A7%8A%E5%A6%B9%E9%A1%B9%E7%9B%AE%E9%93%BE%E6%8E%A5%E5%B8%A6%E6%9C%89%E9%BB%98%E8%AE%A4%E6%90%9C%E7%B4%A2%E7%9A%84%E9%A1%B5%E9%9D%A2" title="Category:使用的姊妹项目链接带有默认搜索的页面">使用的姊妹项目链接带有默认搜索的页面</a></li><li><a href="/wiki/Category:%E5%8C%85%E5%90%ABFAST%E6%A0%87%E8%AF%86%E7%AC%A6%E7%9A%84%E7%BB%B4%E5%9F%BA%E7%99%BE%E7%A7%91%E6%9D%A1%E7%9B%AE" title="Category:包含FAST标识符的维基百科条目">包含FAST标识符的维基百科条目</a></li><li><a href="/wiki/Category:%E5%8C%85%E5%90%ABBNE%E6%A0%87%E8%AF%86%E7%AC%A6%E7%9A%84%E7%BB%B4%E5%9F%BA%E7%99%BE%E7%A7%91%E6%9D%A1%E7%9B%AE" title="Category:包含BNE标识符的维基百科条目">包含BNE标识符的维基百科条目</a></li><li><a href="/wiki/Category:%E5%8C%85%E5%90%ABBNF%E6%A0%87%E8%AF%86%E7%AC%A6%E7%9A%84%E7%BB%B4%E5%9F%BA%E7%99%BE%E7%A7%91%E6%9D%A1%E7%9B%AE" title="Category:包含BNF标识符的维基百科条目">包含BNF标识符的维基百科条目</a></li><li><a href="/wiki/Category:%E5%8C%85%E5%90%ABBNFdata%E6%A0%87%E8%AF%86%E7%AC%A6%E7%9A%84%E7%BB%B4%E5%9F%BA%E7%99%BE%E7%A7%91%E6%9D%A1%E7%9B%AE" title="Category:包含BNFdata标识符的维基百科条目">包含BNFdata标识符的维基百科条目</a></li><li><a href="/wiki/Category:%E5%8C%85%E5%90%ABGND%E6%A0%87%E8%AF%86%E7%AC%A6%E7%9A%84%E7%BB%B4%E5%9F%BA%E7%99%BE%E7%A7%91%E6%9D%A1%E7%9B%AE" title="Category:包含GND标识符的维基百科条目">包含GND标识符的维基百科条目</a></li><li><a href="/wiki/Category:%E5%8C%85%E5%90%ABJ9U%E6%A0%87%E8%AF%86%E7%AC%A6%E7%9A%84%E7%BB%B4%E5%9F%BA%E7%99%BE%E7%A7%91%E6%9D%A1%E7%9B%AE" title="Category:包含J9U标识符的维基百科条目">包含J9U标识符的维基百科条目</a></li><li><a href="/wiki/Category:%E5%8C%85%E5%90%ABLCCN%E6%A0%87%E8%AF%86%E7%AC%A6%E7%9A%84%E7%BB%B4%E5%9F%BA%E7%99%BE%E7%A7%91%E6%9D%A1%E7%9B%AE" title="Category:包含LCCN标识符的维基百科条目">包含LCCN标识符的维基百科条目</a></li><li><a href="/wiki/Category:%E5%8C%85%E5%90%ABNDL%E6%A0%87%E8%AF%86%E7%AC%A6%E7%9A%84%E7%BB%B4%E5%9F%BA%E7%99%BE%E7%A7%91%E6%9D%A1%E7%9B%AE" title="Category:包含NDL标识符的维基百科条目">包含NDL标识符的维基百科条目</a></li><li><a href="/wiki/Category:%E5%8C%85%E5%90%ABNKC%E6%A0%87%E8%AF%86%E7%AC%A6%E7%9A%84%E7%BB%B4%E5%9F%BA%E7%99%BE%E7%A7%91%E6%9D%A1%E7%9B%AE" title="Category:包含NKC标识符的维基百科条目">包含NKC标识符的维基百科条目</a></li><li><a href="/wiki/Category:%E5%8C%85%E5%90%ABSUDOC%E6%A0%87%E8%AF%86%E7%AC%A6%E7%9A%84%E7%BB%B4%E5%9F%BA%E7%99%BE%E7%A7%91%E6%9D%A1%E7%9B%AE" title="Category:包含SUDOC标识符的维基百科条目">包含SUDOC标识符的维基百科条目</a></li></ul></div></div> </div> </main> </div> <div class="mw-footer-container"> <footer id="footer" class="mw-footer" > <ul id="footer-info"> <li id="footer-info-lastmod"> 本页面最后修订于2024年11月5日 (星期二) 02:19。</li> <li id="footer-info-copyright">本站的全部文字在<a rel="nofollow" class="external text" href="//creativecommons.org/licenses/by-sa/4.0/deed.zh">知识共享署名-相同方式共享 4.0协议</a>之条款下提供，附加条款亦可能应用。（请参阅<a class="external text" href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Terms_of_Use">使用条款</a>） Wikipedia®和维基百科标志是<a rel="nofollow" class="external text" href="https://wikimediafoundation.org/zh">维基媒体基金会</a>的注册商标；维基™是维基媒体基金会的商标。 维基媒体基金会是按美国国內稅收法501(c)(3)登记的<a class="external text" href="https://donate.wikimedia.org/wiki/Special:MyLanguage/Tax_deductibility">非营利慈善机构</a>。 </li> </ul> <ul id="footer-places"> <li id="footer-places-privacy"><a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Privacy_policy">隐私政策</a></li> <li id="footer-places-about"><a href="/wiki/Wikipedia:%E5%85%B3%E4%BA%8E">关于维基百科</a></li> <li id="footer-places-disclaimers"><a href="/wiki/Wikipedia:%E5%85%8D%E8%B4%A3%E5%A3%B0%E6%98%8E">免责声明</a></li> <li id="footer-places-wm-codeofconduct"><a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Universal_Code_of_Conduct">行为准则</a></li> <li id="footer-places-developers"><a href="https://developer.wikimedia.org">开发者</a></li> <li id="footer-places-statslink"><a href="https://stats.wikimedia.org/#/zh.wikipedia.org">统计</a></li> <li id="footer-places-cookiestatement"><a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Cookie_statement">Cookie声明</a></li> <li id="footer-places-mobileview"><a href="//zh.m.wikipedia.org/w/index.php?title=%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6&mobileaction=toggle_view_mobile" class="noprint stopMobileRedirectToggle">手机版视图</a></li> </ul> <ul id="footer-icons" class="noprint"> <li id="footer-copyrightico"><a href="https://wikimediafoundation.org/" class="cdx-button cdx-button--fake-button cdx-button--size-large cdx-button--fake-button--enabled"><img src="/static/images/footer/wikimedia-button.svg" width="84" height="29" alt="Wikimedia Foundation" loading="lazy"></a></li> <li id="footer-poweredbyico"><a href="https://www.mediawiki.org/" class="cdx-button cdx-button--fake-button cdx-button--size-large cdx-button--fake-button--enabled"><img src="/w/resources/assets/poweredby_mediawiki.svg" alt="Powered by MediaWiki" width="88" height="31" loading="lazy"></a></li> </ul> </footer> </div> </div> </div> <div class="vector-settings" id="p-dock-bottom"> <ul></ul> </div><script>(RLQ=window.RLQ||[]).push(function(){mw.config.set({"wgHostname":"mw-web.codfw.main-6b8d669998-6ltp6","wgBackendResponseTime":189,"wgPageParseReport":{"limitreport":{"cputime":"1.372","walltime":"1.799","ppvisitednodes":{"value":9899,"limit":1000000},"postexpandincludesize":{"value":375454,"limit":2097152},"templateargumentsize":{"value":10116,"limit":2097152},"expansiondepth":{"value":29,"limit":100},"expensivefunctioncount":{"value":67,"limit":500},"unstrip-depth":{"value":1,"limit":20},"unstrip-size":{"value":173706,"limit":5000000},"entityaccesscount":{"value":1,"limit":400},"timingprofile":["100.00% 1194.583 1 -total"," 26.47% 316.245 1 Template:Reflist"," 13.58% 162.196 1 Template:量子力学"," 13.58% 162.172 2 Template:Navbox"," 13.06% 155.986 1 Template:Sidebar_with_collapsible_lists"," 12.81% 153.029 1 Template:Quantum_mechanics_topics"," 9.85% 117.716 1 Template:Sister_project_links"," 9.39% 112.223 13 Template:Cite_journal"," 8.94% 106.780 47 Template:Le"," 7.80% 93.130 23 Template:Cite_book"]},"scribunto":{"limitreport-timeusage":{"value":"0.587","limit":"10.000"},"limitreport-memusage":{"value":6487233,"limit":52428800}},"cachereport":{"origin":"mw-web.codfw.main-697b7966c5-s282q","timestamp":"20241126182727","ttl":2592000,"transientcontent":false}}});});</script> <script type="application/ld+json">{"@context":"https:\/\/schema.org","@type":"Article","name":"\u91cf\u5b50\u529b\u5b66","url":"https:\/\/zh.wikipedia.org\/wiki\/%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6","sameAs":"http:\/\/www.wikidata.org\/entity\/Q944","mainEntity":"http:\/\/www.wikidata.org\/entity\/Q944","author":{"@type":"Organization","name":"\u7ef4\u57fa\u5a92\u4f53\u9879\u76ee\u8d21\u732e\u8005"},"publisher":{"@type":"Organization","name":"Wikimedia Foundation, Inc.","logo":{"@type":"ImageObject","url":"https:\/\/www.wikimedia.org\/static\/images\/wmf-hor-googpub.png"}},"datePublished":"2003-10-25T17:39:20Z","dateModified":"2024-11-05T02:19:00Z","image":"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/e\/e7\/Hydrogen_Density_Plots.png","headline":"\u7814\u7a76\u5fae\u89c2\u4e16\u754c\u57fa\u672c\u8fd0\u52a8\u89c4\u5f8b\u7684\u7269\u7406\u5b66\u79d1\uff0c\u4e3a\u5f53\u4ee3\u7269\u7406\u6700\u91cd\u8981\u7684\u57fa\u7840\u7406\u8bba\u4e4b\u4e00"}</script> </body> </html>