CINXE.COM

<!DOCTYPE html> <html class="client-nojs vector-feature-language-in-header-enabled vector-feature-language-in-main-page-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-sticky-header-enabled vector-toc-available" lang="en" dir="ltr"> <head> <meta charset="UTF-8"> <title>Atomic, molecular, and optical physics - Wikipedia</title> <script>(function(){var className="client-js vector-feature-language-in-header-enabled vector-feature-language-in-main-page-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-sticky-header-enabled vector-toc-available";var cookie=document.cookie.match(/(?:^|; )enwikimwclientpreferences=([^;]+)/);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":"dmy", "wgMonthNames":["","January","February","March","April","May","June","July","August","September","October","November","December"],"wgRequestId":"93773896-d88e-484e-ad93-3a42dc36972d","wgCanonicalNamespace":"","wgCanonicalSpecialPageName":false,"wgNamespaceNumber":0,"wgPageName":"Atomic,_molecular,_and_optical_physics","wgTitle":"Atomic, molecular, and optical physics","wgCurRevisionId":1245940912,"wgRevisionId":1245940912,"wgArticleId":48579,"wgIsArticle":true,"wgIsRedirect":false,"wgAction":"view","wgUserName":null,"wgUserGroups":["*"],"wgCategories":["Articles with short description","Short description matches Wikidata","Commons category link is on Wikidata","Atomic, molecular, and optical physics"],"wgPageViewLanguage":"en","wgPageContentLanguage":"en","wgPageContentModel":"wikitext","wgRelevantPageName":"Atomic,_molecular,_and_optical_physics","wgRelevantArticleId":48579,"wgIsProbablyEditable":true,"wgRelevantPageIsProbablyEditable":true,"wgRestrictionEdit":[],"wgRestrictionMove":[ ],"wgNoticeProject":"wikipedia","wgCiteReferencePreviewsActive":false,"wgFlaggedRevsParams":{"tags":{"status":{"levels":1}}},"wgMediaViewerOnClick":true,"wgMediaViewerEnabledByDefault":true,"wgPopupsFlags":0,"wgVisualEditor":{"pageLanguageCode":"en","pageLanguageDir":"ltr","pageVariantFallbacks":"en"},"wgMFDisplayWikibaseDescriptions":{"search":true,"watchlist":true,"tagline":false,"nearby":true},"wgWMESchemaEditAttemptStepOversample":false,"wgWMEPageLength":30000,"wgEditSubmitButtonLabelPublish":true,"wgULSPosition":"interlanguage","wgULSisCompactLinksEnabled":false,"wgVector2022LanguageInHeader":true,"wgULSisLanguageSelectorEmpty":false,"wgWikibaseItemId":"Q1151533","wgCheckUserClientHintsHeadersJsApi":["brands","architecture","bitness","fullVersionList","mobile","model","platform","platformVersion"],"GEHomepageSuggestedEditsEnableTopics":true,"wgGETopicsMatchModeEnabled":false,"wgGEStructuredTaskRejectionReasonTextInputEnabled":false,"wgGELevelingUpEnabledForUser":false};RLSTATE={ "ext.globalCssJs.user.styles":"ready","site.styles":"ready","user.styles":"ready","ext.globalCssJs.user":"ready","user":"ready","user.options":"loading","ext.math.styles":"ready","ext.cite.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=["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.ReferenceTooltips","ext.gadget.switcher","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"];</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=en&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=en&modules=startup&only=scripts&raw=1&skin=vector-2022"></script> <meta name="ResourceLoaderDynamicStyles" content=""> <link rel="stylesheet" href="/w/load.php?lang=en&modules=site.styles&only=styles&skin=vector-2022"> <meta name="generator" content="MediaWiki 1.44.0-wmf.16"> <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 name="viewport" content="width=1120"> <meta property="og:title" content="Atomic, molecular, and optical physics - Wikipedia"> <meta property="og:type" content="website"> <link rel="preconnect" href="//upload.wikimedia.org"> <link rel="alternate" media="only screen and (max-width: 640px)" href="//en.m.wikipedia.org/wiki/Atomic,_molecular,_and_optical_physics"> <link rel="alternate" type="application/x-wiki" title="Edit this page" href="/w/index.php?title=Atomic,_molecular,_and_optical_physics&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 (en)"> <link rel="EditURI" type="application/rsd+xml" href="//en.wikipedia.org/w/api.php?action=rsd"> <link rel="canonical" href="https://en.wikipedia.org/wiki/Atomic,_molecular,_and_optical_physics"> <link rel="license" href="https://creativecommons.org/licenses/by-sa/4.0/deed.en"> <link rel="alternate" type="application/atom+xml" title="Wikipedia Atom feed" href="/w/index.php?title=Special:RecentChanges&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-Atomic_molecular_and_optical_physics rootpage-Atomic_molecular_and_optical_physics skin-vector-2022 action-view"><a class="mw-jump-link" href="#bodyContent">Jump to content</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="Site"> <div id="vector-main-menu-dropdown" class="vector-dropdown vector-main-menu-dropdown vector-button-flush-left vector-button-flush-right" title="Main menu" > <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="Main menu" > <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" ><span class="vector-icon mw-ui-icon-menu mw-ui-icon-wikimedia-menu"></span> <span class="vector-dropdown-label-text">Main menu</span> </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">Main menu</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-main-menu.pin">move to sidebar</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-main-menu.unpin">hide</button> </div> <div id="p-navigation" class="vector-menu mw-portlet mw-portlet-navigation" > <div class="vector-menu-heading"> Navigation </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="n-mainpage-description" class="mw-list-item"><a href="/wiki/Main_Page" title="Visit the main page [z]" accesskey="z"><span>Main page</span></a></li><li id="n-contents" class="mw-list-item"><a href="/wiki/Wikipedia:Contents" title="Guides to browsing Wikipedia"><span>Contents</span></a></li><li id="n-currentevents" class="mw-list-item"><a href="/wiki/Portal:Current_events" title="Articles related to current events"><span>Current events</span></a></li><li id="n-randompage" class="mw-list-item"><a href="/wiki/Special:Random" title="Visit a randomly selected article [x]" accesskey="x"><span>Random article</span></a></li><li id="n-aboutsite" class="mw-list-item"><a href="/wiki/Wikipedia:About" title="Learn about Wikipedia and how it works"><span>About Wikipedia</span></a></li><li id="n-contactpage" class="mw-list-item"><a href="//en.wikipedia.org/wiki/Wikipedia:Contact_us" title="How to contact Wikipedia"><span>Contact us</span></a></li> </ul> </div> </div> <div id="p-interaction" class="vector-menu mw-portlet mw-portlet-interaction" > <div class="vector-menu-heading"> Contribute </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="n-help" class="mw-list-item"><a href="/wiki/Help:Contents" title="Guidance on how to use and edit Wikipedia"><span>Help</span></a></li><li id="n-introduction" class="mw-list-item"><a href="/wiki/Help:Introduction" title="Learn how to edit Wikipedia"><span>Learn to edit</span></a></li><li id="n-portal" class="mw-list-item"><a href="/wiki/Wikipedia:Community_portal" title="The hub for editors"><span>Community portal</span></a></li><li id="n-recentchanges" class="mw-list-item"><a href="/wiki/Special:RecentChanges" title="A list of recent changes to Wikipedia [r]" accesskey="r"><span>Recent changes</span></a></li><li id="n-upload" class="mw-list-item"><a href="/wiki/Wikipedia:File_upload_wizard" title="Add images or other media for use on Wikipedia"><span>Upload file</span></a></li><li id="n-specialpages" class="mw-list-item"><a href="/wiki/Special:SpecialPages"><span>Special pages</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> <a href="/wiki/Main_Page" class="mw-logo"> <img class="mw-logo-icon" src="/static/images/icons/wikipedia.png" alt="" aria-hidden="true" height="50" width="50"> <span class="mw-logo-container skin-invert"> <img class="mw-logo-wordmark" alt="Wikipedia" src="/static/images/mobile/copyright/wikipedia-wordmark-en.svg" style="width: 7.5em; height: 1.125em;"> <img class="mw-logo-tagline" alt="The Free Encyclopedia" src="/static/images/mobile/copyright/wikipedia-tagline-en.svg" width="117" height="13" style="width: 7.3125em; height: 0.8125em;"> </span> </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:Search" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only search-toggle" title="Search Wikipedia [f]" accesskey="f"><span class="vector-icon mw-ui-icon-search mw-ui-icon-wikimedia-search"></span> <span>Search</span> </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="Search Wikipedia" aria-label="Search Wikipedia" autocapitalize="sentences" title="Search Wikipedia [f]" accesskey="f" id="searchInput" > <span class="cdx-text-input__icon cdx-text-input__start-icon"></span> </div> <input type="hidden" name="title" value="Special:Search"> </div> <button class="cdx-button cdx-search-input__end-button">Search</button> </form> </div> </div> </div> <nav class="vector-user-links vector-user-links-wide" aria-label="Personal tools"> <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="Appearance"> <div id="vector-appearance-dropdown" class="vector-dropdown " title="Change the appearance of the page's font size, width, and color" > <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="Appearance" > <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" ><span class="vector-icon mw-ui-icon-appearance mw-ui-icon-wikimedia-appearance"></span> <span class="vector-dropdown-label-text">Appearance</span> </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/?wmf_source=donate&wmf_medium=sidebar&wmf_campaign=en.wikipedia.org&uselang=en" class=""><span>Donate</span></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:CreateAccount&returnto=Atomic%2C+molecular%2C+and+optical+physics" title="You are encouraged to create an account and log in; however, it is not mandatory" class=""><span>Create account</span></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:UserLogin&returnto=Atomic%2C+molecular%2C+and+optical+physics" title="You're encouraged to log in; however, it's not mandatory. [o]" accesskey="o" class=""><span>Log in</span></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="Log in and more options" > <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="Personal tools" > <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" ><span class="vector-icon mw-ui-icon-ellipsis mw-ui-icon-wikimedia-ellipsis"></span> <span class="vector-dropdown-label-text">Personal tools</span> </label> <div class="vector-dropdown-content"> <div id="p-personal" class="vector-menu mw-portlet mw-portlet-personal user-links-collapsible-item" title="User menu" > <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/?wmf_source=donate&wmf_medium=sidebar&wmf_campaign=en.wikipedia.org&uselang=en"><span>Donate</span></a></li><li id="pt-createaccount" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Special:CreateAccount&returnto=Atomic%2C+molecular%2C+and+optical+physics" title="You are encouraged to create an account and log in; however, it is not mandatory"><span class="vector-icon mw-ui-icon-userAdd mw-ui-icon-wikimedia-userAdd"></span> <span>Create account</span></a></li><li id="pt-login" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Special:UserLogin&returnto=Atomic%2C+molecular%2C+and+optical+physics" title="You're encouraged to log in; however, it's not mandatory. [o]" accesskey="o"><span class="vector-icon mw-ui-icon-logIn mw-ui-icon-wikimedia-logIn"></span> <span>Log in</span></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"> Pages for logged out editors <a href="/wiki/Help:Introduction" aria-label="Learn more about editing"><span>learn more</span></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:MyContributions" title="A list of edits made from this IP address [y]" accesskey="y"><span>Contributions</span></a></li><li id="pt-anontalk" class="mw-list-item"><a href="/wiki/Special:MyTalk" title="Discussion about edits from this IP address [n]" accesskey="n"><span>Talk</span></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="Site"> <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="Contents" 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">Contents</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">move to sidebar</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">hide</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">(Top)</div> </a> </li> <li id="toc-Atomic_and_molecular_physics" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Atomic_and_molecular_physics"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Atomic and molecular physics</span> </div> </a> <ul id="toc-Atomic_and_molecular_physics-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Optical_physics" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Optical_physics"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Optical physics</span> </div> </a> <ul id="toc-Optical_physics-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-History" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#History"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>History</span> </div> </a> <button aria-controls="toc-History-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle History subsection</span> </button> <ul id="toc-History-sublist" class="vector-toc-list"> <li id="toc-Classical_oscillator_model_of_matter" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Classical_oscillator_model_of_matter"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1</span> <span>Classical oscillator model of matter</span> </div> </a> <ul id="toc-Classical_oscillator_model_of_matter-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Early_quantum_model_of_matter_and_light" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Early_quantum_model_of_matter_and_light"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.2</span> <span>Early quantum model of matter and light</span> </div> </a> <ul id="toc-Early_quantum_model_of_matter_and_light-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Modern_treatments" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Modern_treatments"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Modern treatments</span> </div> </a> <ul id="toc-Modern_treatments-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Isolated_atoms_and_molecules" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Isolated_atoms_and_molecules"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Isolated atoms and molecules</span> </div> </a> <ul id="toc-Isolated_atoms_and_molecules-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Electronic_configuration" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Electronic_configuration"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Electronic configuration</span> </div> </a> <ul id="toc-Electronic_configuration-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>See also</span> </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Notes" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Notes"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>Notes</span> </div> </a> <ul id="toc-Notes-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> <span class="vector-toc-numb">9</span> <span>References</span> </div> </a> <ul id="toc-References-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-External_links" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#External_links"> <div class="vector-toc-text"> <span class="vector-toc-numb">10</span> <span>External links</span> </div> </a> <button aria-controls="toc-External_links-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle External links subsection</span> </button> <ul id="toc-External_links-sublist" class="vector-toc-list"> <li id="toc-Institutions" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Institutions"> <div class="vector-toc-text"> <span class="vector-toc-numb">10.1</span> <span>Institutions</span> </div> </a> <ul id="toc-Institutions-sublist" class="vector-toc-list"> </ul> </li> </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="Contents" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" title="Table of Contents" > <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="Toggle the table of contents" > <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" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Toggle the table of contents</span> </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"><span class="mw-page-title-main">Atomic, molecular, and optical physics</span></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="Go to an article in another language. Available in 24 languages" > <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-24" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">24 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%81%D9%8A%D8%B2%D9%8A%D8%A7%D8%A1_%D8%B0%D8%B1%D9%8A%D8%A9_%D9%88%D8%AC%D8%B2%D9%8A%D8%A6%D9%8A%D8%A9_%D9%88%D8%A8%D8%B5%D8%B1%D9%8A%D8%A9" title="فيزياء ذرية وجزيئية وبصرية – Arabic" lang="ar" hreflang="ar" data-title="فيزياء ذرية وجزيئية وبصرية" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%AA%E0%A6%BE%E0%A6%B0%E0%A6%AE%E0%A6%BE%E0%A6%A3%E0%A6%AC%E0%A6%BF%E0%A6%95,_%E0%A6%86%E0%A6%A3%E0%A6%AC%E0%A6%BF%E0%A6%95_%E0%A6%93_%E0%A6%86%E0%A6%B2%E0%A7%8B%E0%A6%95%E0%A7%80%E0%A6%AF%E0%A6%BC_%E0%A6%AA%E0%A6%A6%E0%A6%BE%E0%A6%B0%E0%A7%8D%E0%A6%A5%E0%A6%AC%E0%A6%BF%E0%A6%9C%E0%A7%8D%E0%A6%9E%E0%A6%BE%E0%A6%A8" title="পারমাণবিক, আণবিক ও আলোকীয় পদার্থবিজ্ঞান – Bangla" lang="bn" hreflang="bn" data-title="পারমাণবিক, আণবিক ও আলোকীয় পদার্থবিজ্ঞান" data-language-autonym="বাংলা" data-language-local-name="Bangla" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%A4%D1%96%D0%B7%D1%96%D0%BA%D0%B0_%D0%B0%D1%82%D0%B0%D0%BC%D0%B0%D1%9E_%D1%96_%D0%BC%D0%B0%D0%BB%D0%B5%D0%BA%D1%83%D0%BB" title="Фізіка атамаў і малекул – Belarusian" lang="be" hreflang="be" data-title="Фізіка атамаў і малекул" data-language-autonym="Беларуская" data-language-local-name="Belarusian" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%90%D1%82%D0%BE%D0%BC%D0%BD%D0%B0,_%D0%BC%D0%BE%D0%BB%D0%B5%D0%BA%D1%83%D0%BB%D1%8F%D1%80%D0%BD%D0%B0_%D0%B8_%D0%BE%D0%BF%D1%82%D0%B8%D1%87%D0%BD%D0%B0_%D1%84%D0%B8%D0%B7%D0%B8%D0%BA%D0%B0" title="Атомна, молекулярна и оптична физика – Bulgarian" lang="bg" hreflang="bg" data-title="Атомна, молекулярна и оптична физика" data-language-autonym="Български" data-language-local-name="Bulgarian" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%90%D1%82%D0%BE%D0%BC%D1%81%D0%B5%D0%BD_%D1%82%D0%B0%D1%82%D0%B0_%D0%BC%D0%BE%D0%BB%D0%B5%D0%BA%D1%83%D0%BB%C4%83%D1%81%D0%B5%D0%BD_%D1%84%D0%B8%D0%B7%D0%B8%D0%BA%D0%B8" title="Атомсен тата молекулăсен физики – Chuvash" lang="cv" hreflang="cv" data-title="Атомсен тата молекулăсен физики" data-language-autonym="Чӑвашла" data-language-local-name="Chuvash" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Atomov%C3%A1,_molekulov%C3%A1_a_optick%C3%A1_fyzika" title="Atomová, molekulová a optická fyzika – Czech" lang="cs" hreflang="cs" data-title="Atomová, molekulová a optická fyzika" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D9%81%DB%8C%D8%B2%DB%8C%DA%A9_%D8%A7%D8%AA%D9%85%DB%8C%D8%8C_%D9%85%D9%88%D9%84%DA%A9%D9%88%D9%84%DB%8C_%D9%88_%D9%86%D9%88%D8%B1%DB%8C" title="فیزیک اتمی، مولکولی و نوری – Persian" lang="fa" hreflang="fa" data-title="فیزیک اتمی، مولکولی و نوری" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%9B%90%EC%9E%90_%EB%B6%84%EC%9E%90_%EA%B4%91_%EB%AC%BC%EB%A6%AC%ED%95%99" title="원자 분자 광 물리학 – Korean" lang="ko" hreflang="ko" data-title="원자 분자 광 물리학" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Fisika_atomik,_molekul,_dan_optik" title="Fisika atomik, molekul, dan optik – Indonesian" lang="id" hreflang="id" data-title="Fisika atomik, molekul, dan optik" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesian" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-ky mw-list-item"><a href="https://ky.wikipedia.org/wiki/%D0%90%D1%82%D0%BE%D0%BC%D0%B4%D1%83%D0%BA_%D0%BC%D0%BE%D0%BB%D0%B5%D0%BA%D1%83%D0%BB%D1%8F%D1%80%D0%B4%D1%8B%D0%BA_%D0%BE%D0%BA%D1%83%D1%83" title="Атомдук молекулярдык окуу – Kyrgyz" lang="ky" hreflang="ky" data-title="Атомдук молекулярдык окуу" data-language-autonym="Кыргызча" data-language-local-name="Kyrgyz" class="interlanguage-link-target"><span>Кыргызча</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%90%D1%82%D0%BE%D0%BC%D1%81%D0%BA%D0%B0,_%D0%BC%D0%BE%D0%BB%D0%B5%D0%BA%D1%83%D0%BB%D0%B0%D1%80%D0%BD%D0%B0_%D0%B8_%D0%BE%D0%BF%D1%82%D0%B8%D1%87%D0%BA%D0%B0_%D1%84%D0%B8%D0%B7%D0%B8%D0%BA%D0%B0" title="Атомска, молекуларна и оптичка физика – Macedonian" lang="mk" hreflang="mk" data-title="Атомска, молекуларна и оптичка физика" data-language-autonym="Македонски" data-language-local-name="Macedonian" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Fizik_atom,_molekul,_dan_optik" title="Fizik atom, molekul, dan optik – Malay" lang="ms" hreflang="ms" data-title="Fizik atom, molekul, dan optik" data-language-autonym="Bahasa Melayu" data-language-local-name="Malay" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-ce mw-list-item"><a href="https://ce.wikipedia.org/wiki/%D0%90%D1%82%D0%BE%D0%BC%D0%B8%D0%B9%D0%BD_%D0%B0,_%D0%BC%D0%BE%D0%BB%D0%B5%D0%BA%D1%83%D0%BB%D0%B8%D0%B9%D0%BD_%D0%B0_%D1%84%D0%B8%D0%B7%D0%B8%D0%BA%D0%B0" title="Атомийн а, молекулийн а физика – Chechen" lang="ce" hreflang="ce" data-title="Атомийн а, молекулийн а физика" data-language-autonym="Нохчийн" data-language-local-name="Chechen" class="interlanguage-link-target"><span>Нохчийн</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Fizic%C4%83_atomic%C4%83_%C8%99i_molecular%C4%83" title="Fizică atomică și moleculară – Romanian" lang="ro" hreflang="ro" data-title="Fizică atomică și moleculară" data-language-autonym="Română" data-language-local-name="Romanian" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%A4%D0%B8%D0%B7%D0%B8%D0%BA%D0%B0_%D0%B0%D1%82%D0%BE%D0%BC%D0%BE%D0%B2_%D0%B8_%D0%BC%D0%BE%D0%BB%D0%B5%D0%BA%D1%83%D0%BB" title="Физика атомов и молекул – Russian" lang="ru" hreflang="ru" data-title="Физика атомов и молекул" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/At%C3%B3mov%C3%A1,_molekulov%C3%A1_a_optick%C3%A1_fyzika" title="Atómová, molekulová a optická fyzika – Slovak" lang="sk" hreflang="sk" data-title="Atómová, molekulová a optická fyzika" data-language-autonym="Slovenčina" data-language-local-name="Slovak" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Atomska,_molekulska_in_opti%C4%8Dna_fizika" title="Atomska, molekulska in optična fizika – Slovenian" lang="sl" hreflang="sl" data-title="Atomska, molekulska in optična fizika" data-language-autonym="Slovenščina" data-language-local-name="Slovenian" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%85%E0%AE%A3%E0%AF%81,_%E0%AE%AE%E0%AF%82%E0%AE%B2%E0%AE%95%E0%AF%8D%E0%AE%95%E0%AF%82%E0%AE%B1%E0%AF%81,_%E0%AE%92%E0%AE%B3%E0%AE%BF_%E0%AE%87%E0%AE%AF%E0%AE%B1%E0%AF%8D%E0%AE%AA%E0%AE%BF%E0%AE%AF%E0%AE%B2%E0%AF%8D" title="அணு, மூலக்கூறு, ஒளி இயற்பியல் – Tamil" lang="ta" hreflang="ta" data-title="அணு, மூலக்கூறு, ஒளி இயற்பியல்" data-language-autonym="தமிழ்" data-language-local-name="Tamil" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%9F%E0%B8%B4%E0%B8%AA%E0%B8%B4%E0%B8%81%E0%B8%AA%E0%B9%8C%E0%B8%AD%E0%B8%B0%E0%B8%95%E0%B8%AD%E0%B8%A1_%E0%B9%82%E0%B8%A1%E0%B9%80%E0%B8%A5%E0%B8%81%E0%B8%B8%E0%B8%A5_%E0%B9%81%E0%B8%A5%E0%B8%B0%E0%B8%97%E0%B8%B1%E0%B8%A8%E0%B8%99%E0%B8%A8%E0%B8%B2%E0%B8%AA%E0%B8%95%E0%B8%A3%E0%B9%8C" title="ฟิสิกส์อะตอม โมเลกุล และทัศนศาสตร์ – Thai" lang="th" hreflang="th" data-title="ฟิสิกส์อะตอม โมเลกุล และทัศนศาสตร์" data-language-autonym="ไทย" data-language-local-name="Thai" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Atomik,_molek%C3%BCler_ve_optik_fizik" title="Atomik, moleküler ve optik fizik – Turkish" lang="tr" hreflang="tr" data-title="Atomik, moleküler ve optik fizik" data-language-autonym="Türkçe" data-language-local-name="Turkish" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%90%D1%82%D0%BE%D0%BC%D0%BD%D0%B0,_%D0%BC%D0%BE%D0%BB%D0%B5%D0%BA%D1%83%D0%BB%D1%8F%D1%80%D0%BD%D0%B0_%D1%96_%D0%BE%D0%BF%D1%82%D0%B8%D1%87%D0%BD%D0%B0_%D1%84%D1%96%D0%B7%D0%B8%D0%BA%D0%B0" title="Атомна, молекулярна і оптична фізика – Ukrainian" lang="uk" hreflang="uk" data-title="Атомна, молекулярна і оптична фізика" data-language-autonym="Українська" data-language-local-name="Ukrainian" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/V%E1%BA%ADt_l%C3%BD_nguy%C3%AAn_t%E1%BB%AD,_ph%C3%A2n_t%E1%BB%AD_v%C3%A0_quang_h%E1%BB%8Dc" title="Vật lý nguyên tử, phân tử và quang học – Vietnamese" lang="vi" hreflang="vi" data-title="Vật lý nguyên tử, phân tử và quang học" data-language-autonym="Tiếng Việt" data-language-local-name="Vietnamese" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E5%8E%9F%E5%AD%90%E5%88%86%E5%AD%90%E5%90%8C%E5%85%89%E7%89%A9%E7%90%86%E5%AD%B8" title="原子分子同光物理學 – Cantonese" lang="yue" hreflang="yue" data-title="原子分子同光物理學" data-language-autonym="粵語" data-language-local-name="Cantonese" class="interlanguage-link-target"><span>粵語</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/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 – Chinese" lang="zh" hreflang="zh" data-title="原子分子与光物理学" data-language-autonym="中文" data-language-local-name="Chinese" class="interlanguage-link-target"><span>中文</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q1151533#sitelinks-wikipedia" title="Edit interlanguage links" class="wbc-editpage">Edit links</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div id="left-navigation"> <nav aria-label="Namespaces"> <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/Atomic,_molecular,_and_optical_physics" title="View the content page [c]" accesskey="c"><span>Article</span></a></li><li id="ca-talk" class="vector-tab-noicon mw-list-item"><a href="/wiki/Talk:Atomic,_molecular,_and_optical_physics" rel="discussion" title="Discuss improvements to the content page [t]" accesskey="t"><span>Talk</span></a></li> </ul> </div> </div> <div id="vector-variants-dropdown" class="vector-dropdown emptyPortlet" > <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="Change language variant" > <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" ><span class="vector-dropdown-label-text">English</span> </label> <div class="vector-dropdown-content"> <div id="p-variants" class="vector-menu mw-portlet mw-portlet-variants emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> </div> </div> </nav> </div> <div id="right-navigation" class="vector-collapsible"> <nav aria-label="Views"> <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/Atomic,_molecular,_and_optical_physics"><span>Read</span></a></li><li id="ca-edit" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Atomic,_molecular,_and_optical_physics&action=edit" title="Edit this page [e]" accesskey="e"><span>Edit</span></a></li><li id="ca-history" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Atomic,_molecular,_and_optical_physics&action=history" title="Past revisions of this page [h]" accesskey="h"><span>View history</span></a></li> </ul> </div> </div> </nav> <nav class="vector-page-tools-landmark" aria-label="Page tools"> <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="Tools" > <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" ><span class="vector-dropdown-label-text">Tools</span> </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">Tools</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-page-tools.pin">move to sidebar</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-page-tools.unpin">hide</button> </div> <div id="p-cactions" class="vector-menu mw-portlet mw-portlet-cactions emptyPortlet vector-has-collapsible-items" title="More options" > <div class="vector-menu-heading"> Actions </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/Atomic,_molecular,_and_optical_physics"><span>Read</span></a></li><li id="ca-more-edit" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Atomic,_molecular,_and_optical_physics&action=edit" title="Edit this page [e]" accesskey="e"><span>Edit</span></a></li><li id="ca-more-history" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Atomic,_molecular,_and_optical_physics&action=history"><span>View history</span></a></li> </ul> </div> </div> <div id="p-tb" class="vector-menu mw-portlet mw-portlet-tb" > <div class="vector-menu-heading"> General </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="t-whatlinkshere" class="mw-list-item"><a href="/wiki/Special:WhatLinksHere/Atomic,_molecular,_and_optical_physics" title="List of all English Wikipedia pages containing links to this page [j]" accesskey="j"><span>What links here</span></a></li><li id="t-recentchangeslinked" class="mw-list-item"><a href="/wiki/Special:RecentChangesLinked/Atomic,_molecular,_and_optical_physics" rel="nofollow" title="Recent changes in pages linked from this page [k]" accesskey="k"><span>Related changes</span></a></li><li id="t-upload" class="mw-list-item"><a href="//en.wikipedia.org/wiki/Wikipedia:File_Upload_Wizard" title="Upload files [u]" accesskey="u"><span>Upload file</span></a></li><li id="t-permalink" class="mw-list-item"><a href="/w/index.php?title=Atomic,_molecular,_and_optical_physics&oldid=1245940912" title="Permanent link to this revision of this page"><span>Permanent link</span></a></li><li id="t-info" class="mw-list-item"><a href="/w/index.php?title=Atomic,_molecular,_and_optical_physics&action=info" title="More information about this page"><span>Page information</span></a></li><li id="t-cite" class="mw-list-item"><a href="/w/index.php?title=Special:CiteThisPage&page=Atomic%2C_molecular%2C_and_optical_physics&id=1245940912&wpFormIdentifier=titleform" title="Information on how to cite this page"><span>Cite this page</span></a></li><li id="t-urlshortener" class="mw-list-item"><a href="/w/index.php?title=Special:UrlShortener&url=https%3A%2F%2Fen.wikipedia.org%2Fwiki%2FAtomic%2C_molecular%2C_and_optical_physics"><span>Get shortened URL</span></a></li><li id="t-urlshortener-qrcode" class="mw-list-item"><a href="/w/index.php?title=Special:QrCode&url=https%3A%2F%2Fen.wikipedia.org%2Fwiki%2FAtomic%2C_molecular%2C_and_optical_physics"><span>Download QR code</span></a></li> </ul> </div> </div> <div id="p-coll-print_export" class="vector-menu mw-portlet mw-portlet-coll-print_export" > <div class="vector-menu-heading"> Print/export </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="coll-download-as-rl" class="mw-list-item"><a href="/w/index.php?title=Special:DownloadAsPdf&page=Atomic%2C_molecular%2C_and_optical_physics&action=show-download-screen" title="Download this page as a PDF file"><span>Download as PDF</span></a></li><li id="t-print" class="mw-list-item"><a href="/w/index.php?title=Atomic,_molecular,_and_optical_physics&printable=yes" title="Printable version of this page [p]" accesskey="p"><span>Printable version</span></a></li> </ul> </div> </div> <div id="p-wikibase-otherprojects" class="vector-menu mw-portlet mw-portlet-wikibase-otherprojects" > <div class="vector-menu-heading"> In other projects </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:Atomic,_molecular,_and_optical_physics" hreflang="en"><span>Wikimedia Commons</span></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/Q1151533" title="Structured data on this page hosted by Wikidata [g]" accesskey="g"><span>Wikidata item</span></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="Page tools"> <div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="Appearance"> <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">Appearance</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">move to sidebar</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">hide</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> <div id="siteSub" class="noprint">From Wikipedia, the free encyclopedia</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Study of matter-light interactions at small scales</div> <style data-mw-deduplicate="TemplateStyles:r1129693374">.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 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 dd dd:first-child::before,.mw-parser-output .hlist dd dt:first-child::before,.mw-parser-output .hlist dd li:first-child::before,.mw-parser-output .hlist dt dd:first-child::before,.mw-parser-output .hlist dt dt:first-child::before,.mw-parser-output .hlist dt li:first-child::before,.mw-parser-output .hlist li dd:first-child::before,.mw-parser-output .hlist li dt:first-child::before,.mw-parser-output .hlist li li:first-child::before{content:" (";font-weight:normal}.mw-parser-output .hlist dd dd:last-child::after,.mw-parser-output .hlist dd dt:last-child::after,.mw-parser-output .hlist dd li:last-child::after,.mw-parser-output .hlist dt dd:last-child::after,.mw-parser-output .hlist dt dt:last-child::after,.mw-parser-output .hlist dt li:last-child::after,.mw-parser-output .hlist li dd:last-child::after,.mw-parser-output .hlist li dt:last-child::after,.mw-parser-output .hlist li li:last-child::after{content:")";font-weight:normal}.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 "}</style><style data-mw-deduplicate="TemplateStyles:r1126788409">.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:r1246091330">.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:115%;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-title-with-pretitle{background:transparent!important}html.skin-theme-clientpref-night .mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle a{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-title-with-pretitle{background:transparent!important}html.skin-theme-clientpref-os .mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle a{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:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><table class="sidebar sidebar-collapse nomobile nowraplinks plainlist nowraplinks" style="width:19.0em;"><tbody><tr><td class="sidebar-pretitle">Part of a series of articles about</td></tr><tr><th class="sidebar-title-with-pretitle"><a href="/wiki/Quantum_mechanics" title="Quantum mechanics">Quantum mechanics</a></th></tr><tr><td class="sidebar-image"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle i\hbar {\frac {d}{dt}}|\Psi \rangle ={\hat {H}}|\Psi \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>d</mi> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi mathvariant="normal">Ψ</mi> <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 mathvariant="normal">Ψ</mi> <mo fence="false" stretchy="false">⟩</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle i\hbar {\frac {d}{dt}}|\Psi \rangle ={\hat {H}}|\Psi \rangle }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1799e4a910c7d26396922a20ef5ceec25ca1871c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:16.882ex; height:5.509ex;" alt="{\displaystyle i\hbar {\frac {d}{dt}}|\Psi \rangle ={\hat {H}}|\Psi \rangle }"></span><div class="sidebar-caption" style="font-size:90%;padding-top:0.4em;font-style:italic;"><a href="/wiki/Schr%C3%B6dinger_equation" title="Schrödinger equation">Schrödinger equation</a></div></td></tr><tr><td class="sidebar-above hlist nowrap" style="display:block;margin-bottom:0.4em;"> <ul><li><a href="/wiki/Introduction_to_quantum_mechanics" title="Introduction to quantum mechanics">Introduction</a></li> <li><a href="/wiki/Glossary_of_elementary_quantum_mechanics" title="Glossary of elementary quantum mechanics">Glossary</a></li> <li><a href="/wiki/History_of_quantum_mechanics" title="History of quantum mechanics">History</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;;color: var(--color-base)">Background</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/Classical_mechanics" title="Classical mechanics">Classical mechanics</a></li> <li><a href="/wiki/Old_quantum_theory" title="Old quantum theory">Old quantum theory</a></li> <li><a href="/wiki/Bra%E2%80%93ket_notation" title="Bra–ket notation">Bra–ket notation</a></li></ul> <div class="hlist"> <ul><li><a href="/wiki/Hamiltonian_(quantum_mechanics)" title="Hamiltonian (quantum mechanics)">Hamiltonian</a></li> <li><a href="/wiki/Wave_interference" title="Wave interference">Interference</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;;color: var(--color-base)">Fundamentals</div><div class="sidebar-list-content mw-collapsible-content" style="border-top:1px solid #aaa;border-bottom:1px solid #aaa;"><div class="hlist"> <ul><li><a href="/wiki/Complementarity_(physics)" title="Complementarity (physics)">Complementarity</a></li> <li><a href="/wiki/Quantum_decoherence" title="Quantum decoherence">Decoherence</a></li> <li><a href="/wiki/Quantum_entanglement" title="Quantum entanglement">Entanglement</a></li> <li><a href="/wiki/Energy_level" title="Energy level">Energy level</a></li> <li><a href="/wiki/Measurement_in_quantum_mechanics" title="Measurement in quantum mechanics">Measurement</a></li> <li><a href="/wiki/Quantum_nonlocality" title="Quantum nonlocality">Nonlocality</a></li> <li><a href="/wiki/Quantum_number" title="Quantum number">Quantum number</a></li> <li><a href="/wiki/Quantum_state" title="Quantum state">State</a></li> <li><a href="/wiki/Quantum_superposition" title="Quantum superposition">Superposition</a></li> <li><a href="/wiki/Symmetry_in_quantum_mechanics" title="Symmetry in quantum mechanics">Symmetry</a></li> <li><a href="/wiki/Quantum_tunnelling" title="Quantum tunnelling">Tunnelling</a></li> <li><a href="/wiki/Uncertainty_principle" title="Uncertainty principle">Uncertainty</a></li> <li><a href="/wiki/Wave_function" title="Wave function">Wave function</a> <ul><li><a href="/wiki/Wave_function_collapse" title="Wave function collapse">Collapse</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;;color: var(--color-base)">Experiments</div><div class="sidebar-list-content mw-collapsible-content" style="border-top:1px solid #aaa;border-bottom:1px solid #aaa;"><div class="hlist"> <ul><li><a href="/wiki/Bell_test" title="Bell test">Bell's inequality</a></li> <li><a href="/wiki/CHSH_inequality" title="CHSH inequality">CHSH inequality</a></li> <li><a href="/wiki/Davisson%E2%80%93Germer_experiment" title="Davisson–Germer experiment">Davisson–Germer</a></li> <li><a href="/wiki/Double-slit_experiment" title="Double-slit experiment">Double-slit</a></li> <li><a href="/wiki/Elitzur%E2%80%93Vaidman_bomb_tester" title="Elitzur–Vaidman bomb tester">Elitzur–Vaidman</a></li> <li><a href="/wiki/Franck%E2%80%93Hertz_experiment" title="Franck–Hertz experiment">Franck–Hertz</a></li> <li><a href="/wiki/Leggett_inequality" title="Leggett inequality">Leggett inequality</a></li> <li><a href="/wiki/Leggett%E2%80%93Garg_inequality" title="Leggett–Garg inequality">Leggett–Garg inequality</a></li> <li><a href="/wiki/Mach%E2%80%93Zehnder_interferometer" title="Mach–Zehnder interferometer">Mach–Zehnder</a></li> <li><a href="/wiki/Popper%27s_experiment" title="Popper's experiment">Popper</a></li></ul> </div> <ul><li><a href="/wiki/Quantum_eraser_experiment" title="Quantum eraser experiment">Quantum eraser</a> <ul><li><a href="/wiki/Delayed-choice_quantum_eraser" title="Delayed-choice quantum eraser">Delayed-choice</a></li></ul></li></ul> <div class="hlist"> <ul><li><a href="/wiki/Schr%C3%B6dinger%27s_cat" title="Schrödinger's cat">Schrödinger's cat</a></li> <li><a href="/wiki/Stern%E2%80%93Gerlach_experiment" title="Stern–Gerlach experiment">Stern–Gerlach</a></li> <li><a href="/wiki/Wheeler%27s_delayed-choice_experiment" title="Wheeler's delayed-choice experiment">Wheeler's delayed-choice</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;;color: var(--color-base)">Formulations</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/Mathematical_formulation_of_quantum_mechanics" title="Mathematical formulation of quantum mechanics">Overview</a></li></ul> <div class="hlist"> <ul><li><a href="/wiki/Heisenberg_picture" title="Heisenberg picture">Heisenberg</a></li> <li><a href="/wiki/Interaction_picture" title="Interaction picture">Interaction</a></li> <li><a href="/wiki/Matrix_mechanics" title="Matrix mechanics">Matrix</a></li> <li><a href="/wiki/Phase-space_formulation" title="Phase-space formulation">Phase-space</a></li> <li><a href="/wiki/Schr%C3%B6dinger_picture" title="Schrödinger picture">Schrödinger</a></li> <li><a href="/wiki/Path_integral_formulation" title="Path integral formulation">Sum-over-histories (path integral)</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;;color: var(--color-base)">Equations</div><div class="sidebar-list-content mw-collapsible-content" style="border-top:1px solid #aaa;border-bottom:1px solid #aaa;"><div class="hlist"> <ul><li><a href="/wiki/Dirac_equation" title="Dirac equation">Dirac</a></li> <li><a href="/wiki/Klein%E2%80%93Gordon_equation" title="Klein–Gordon equation">Klein–Gordon</a></li> <li><a href="/wiki/Pauli_equation" title="Pauli equation">Pauli</a></li> <li><a href="/wiki/Rydberg_formula" title="Rydberg formula">Rydberg</a></li> <li><a href="/wiki/Schr%C3%B6dinger_equation" title="Schrödinger equation">Schrödinger</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;;color: var(--color-base)"><a href="/wiki/Interpretations_of_quantum_mechanics" title="Interpretations of quantum mechanics">Interpretations</a></div><div class="sidebar-list-content mw-collapsible-content" style="border-top:1px solid #aaa;border-bottom:1px solid #aaa;"><div class="hlist"> <ul><li><a href="/wiki/Quantum_Bayesianism" title="Quantum Bayesianism">Bayesian</a></li> <li><a href="/wiki/Consistent_histories" title="Consistent histories">Consistent histories</a></li> <li><a href="/wiki/Copenhagen_interpretation" title="Copenhagen interpretation">Copenhagen</a></li> <li><a href="/wiki/De_Broglie%E2%80%93Bohm_theory" title="De Broglie–Bohm theory">de Broglie–Bohm</a></li> <li><a href="/wiki/Ensemble_interpretation" title="Ensemble interpretation">Ensemble</a></li> <li><a href="/wiki/Hidden-variable_theory" title="Hidden-variable theory">Hidden-variable</a> <ul><li><a href="/wiki/Local_hidden-variable_theory" title="Local hidden-variable theory">Local</a> <ul><li><a href="/wiki/Superdeterminism" title="Superdeterminism">Superdeterminism</a></li></ul></li></ul></li> <li><a href="/wiki/Many-worlds_interpretation" title="Many-worlds interpretation">Many-worlds</a></li> <li><a href="/wiki/Objective-collapse_theory" title="Objective-collapse theory">Objective-collapse</a></li> <li><a href="/wiki/Quantum_logic" title="Quantum logic">Quantum logic</a></li> <li><a href="/wiki/Relational_quantum_mechanics" title="Relational quantum mechanics">Relational</a></li> <li><a href="/wiki/Transactional_interpretation" title="Transactional interpretation">Transactional</a></li> <li><a href="/wiki/Von_Neumann%E2%80%93Wigner_interpretation" title="Von Neumann–Wigner interpretation">Von Neumann–Wigner</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;;color: var(--color-base)">Advanced topics</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/Relativistic_quantum_mechanics" title="Relativistic quantum mechanics">Relativistic quantum mechanics</a></li> <li><a href="/wiki/Quantum_field_theory" title="Quantum field theory">Quantum field theory</a></li> <li><a href="/wiki/Quantum_information_science" title="Quantum information science">Quantum information science</a></li> <li><a href="/wiki/Quantum_computing" title="Quantum computing">Quantum computing</a></li> <li><a href="/wiki/Quantum_chaos" title="Quantum chaos">Quantum chaos</a></li> <li><a href="/wiki/Einstein%E2%80%93Podolsky%E2%80%93Rosen_paradox" title="Einstein–Podolsky–Rosen paradox">EPR paradox</a></li> <li><a href="/wiki/Density_matrix" title="Density matrix">Density matrix</a></li> <li><a href="/wiki/Scattering_theory" class="mw-redirect" title="Scattering theory">Scattering theory</a></li> <li><a href="/wiki/Quantum_statistical_mechanics" title="Quantum statistical mechanics">Quantum statistical mechanics</a></li> <li><a href="/wiki/Quantum_machine_learning" title="Quantum machine learning">Quantum machine learning</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;;color: var(--color-base)">Scientists</div><div class="sidebar-list-content mw-collapsible-content" style="border-top:1px solid #aaa;border-bottom:1px solid #aaa;"><div class="hlist"> <ul><li><a href="/wiki/Yakir_Aharonov" title="Yakir Aharonov">Aharonov</a></li> <li><a href="/wiki/John_Stewart_Bell" title="John Stewart Bell">Bell</a></li> <li><a href="/wiki/Hans_Bethe" title="Hans Bethe">Bethe</a></li> <li><a href="/wiki/Patrick_Blackett" title="Patrick Blackett">Blackett</a></li> <li><a href="/wiki/Felix_Bloch" title="Felix Bloch">Bloch</a></li> <li><a href="/wiki/David_Bohm" title="David Bohm">Bohm</a></li> <li><a href="/wiki/Niels_Bohr" title="Niels Bohr">Bohr</a></li> <li><a href="/wiki/Max_Born" title="Max Born">Born</a></li> <li><a href="/wiki/Satyendra_Nath_Bose" title="Satyendra Nath Bose">Bose</a></li> <li><a href="/wiki/Louis_de_Broglie" title="Louis de Broglie">de Broglie</a></li> <li><a href="/wiki/Arthur_Compton" title="Arthur Compton">Compton</a></li> <li><a href="/wiki/Paul_Dirac" title="Paul Dirac">Dirac</a></li> <li><a href="/wiki/Clinton_Davisson" title="Clinton Davisson">Davisson</a></li> <li><a href="/wiki/Peter_Debye" title="Peter Debye">Debye</a></li> <li><a href="/wiki/Paul_Ehrenfest" title="Paul Ehrenfest">Ehrenfest</a></li> <li><a href="/wiki/Albert_Einstein" title="Albert Einstein">Einstein</a></li> <li><a href="/wiki/Hugh_Everett_III" title="Hugh Everett III">Everett</a></li> <li><a href="/wiki/Vladimir_Fock" title="Vladimir Fock">Fock</a></li> <li><a href="/wiki/Enrico_Fermi" title="Enrico Fermi">Fermi</a></li> <li><a href="/wiki/Richard_Feynman" title="Richard Feynman">Feynman</a></li> <li><a href="/wiki/Roy_J._Glauber" title="Roy J. Glauber">Glauber</a></li> <li><a href="/wiki/Martin_Gutzwiller" title="Martin Gutzwiller">Gutzwiller</a></li> <li><a href="/wiki/Werner_Heisenberg" title="Werner Heisenberg">Heisenberg</a></li> <li><a href="/wiki/David_Hilbert" title="David Hilbert">Hilbert</a></li> <li><a href="/wiki/Pascual_Jordan" title="Pascual Jordan">Jordan</a></li> <li><a href="/wiki/Hans_Kramers" title="Hans Kramers">Kramers</a></li> <li><a href="/wiki/Willis_Lamb" title="Willis Lamb">Lamb</a></li> <li><a href="/wiki/Lev_Landau" title="Lev Landau">Landau</a></li> <li><a href="/wiki/Max_von_Laue" title="Max von Laue">Laue</a></li> <li><a href="/wiki/Henry_Moseley" title="Henry Moseley">Moseley</a></li> <li><a href="/wiki/Robert_Andrews_Millikan" title="Robert Andrews Millikan">Millikan</a></li> <li><a href="/wiki/Heike_Kamerlingh_Onnes" title="Heike Kamerlingh Onnes">Onnes</a></li> <li><a href="/wiki/Wolfgang_Pauli" title="Wolfgang Pauli">Pauli</a></li> <li><a href="/wiki/Max_Planck" title="Max Planck">Planck</a></li> <li><a href="/wiki/Isidor_Isaac_Rabi" title="Isidor Isaac Rabi">Rabi</a></li> <li><a href="/wiki/C._V._Raman" title="C. V. Raman">Raman</a></li> <li><a href="/wiki/Johannes_Rydberg" title="Johannes Rydberg">Rydberg</a></li> <li><a href="/wiki/Erwin_Schr%C3%B6dinger" title="Erwin Schrödinger">Schrödinger</a></li> <li><a href="/wiki/Michelle_Simmons" title="Michelle Simmons">Simmons</a></li> <li><a href="/wiki/Arnold_Sommerfeld" title="Arnold Sommerfeld">Sommerfeld</a></li> <li><a href="/wiki/John_von_Neumann" title="John von Neumann">von Neumann</a></li> <li><a href="/wiki/Hermann_Weyl" title="Hermann Weyl">Weyl</a></li> <li><a href="/wiki/Wilhelm_Wien" title="Wilhelm Wien">Wien</a></li> <li><a href="/wiki/Eugene_Wigner" title="Eugene Wigner">Wigner</a></li> <li><a href="/wiki/Pieter_Zeeman" title="Pieter Zeeman">Zeeman</a></li> <li><a href="/wiki/Anton_Zeilinger" title="Anton Zeilinger">Zeilinger</a></li></ul> </div></div></div></td> </tr><tr><td class="sidebar-navbar" style="border-top:1px solid #aaa;padding-top:0.1em;"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><style data-mw-deduplicate="TemplateStyles:r1239400231">.mw-parser-output .navbar{display:inline;font-size:88%;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:114%;margin:0 7em}.mw-parser-output .navbar-ct-mini{font-size:114%;margin:0 4em}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:Quantum_mechanics" title="Template:Quantum mechanics"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Quantum_mechanics" title="Template talk:Quantum mechanics"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Quantum_mechanics" title="Special:EditPage/Template:Quantum mechanics"><abbr title="Edit this template">e</abbr></a></li></ul></div></td></tr></tbody></table> <p><b>Atomic, molecular, and optical physics</b> (<b>AMO</b>) is the study of <a href="/wiki/Matter" title="Matter">matter</a>–matter and <a href="/wiki/Light" title="Light">light</a>–matter interactions, at the scale of one or a few <a href="/wiki/Atom" title="Atom">atoms</a><sup id="cite_ref-nap_1-0" class="reference"><a href="#cite_note-nap-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> and energy scales around several <a href="/wiki/Electron_volt" class="mw-redirect" title="Electron volt">electron volts</a>.<sup id="cite_ref-Drake_2-0" class="reference"><a href="#cite_note-Drake-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 1356">: 1356 </span></sup><sup id="cite_ref-chen_3-0" class="reference"><a href="#cite_note-chen-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> The three areas are closely interrelated. AMO theory includes <a href="/wiki/Classical_physics" title="Classical physics">classical</a>, <a href="/wiki/Semiclassical_physics" title="Semiclassical physics">semi-classical</a> and <a href="/wiki/Quantum_physics" class="mw-redirect" title="Quantum physics">quantum</a> treatments. Typically, the theory and applications of <a href="/wiki/Emission_spectrum" title="Emission spectrum">emission</a>, <a href="/wiki/Absorption_(electromagnetic_radiation)" title="Absorption (electromagnetic radiation)">absorption</a>, <a href="/wiki/Scattering" title="Scattering">scattering</a> of <a href="/wiki/Electromagnetic_radiation" title="Electromagnetic radiation">electromagnetic radiation</a> (light) from <a href="/wiki/Excited_state" title="Excited state">excited</a> <a href="/wiki/Atom" title="Atom">atoms</a> and <a href="/wiki/Molecule" title="Molecule">molecules</a>, analysis of spectroscopy, generation of <a href="/wiki/Laser" title="Laser">lasers</a> and <a href="/wiki/Maser" title="Maser">masers</a>, and the optical properties of matter in general, fall into these categories. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Atomic_and_molecular_physics">Atomic and molecular physics</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Atomic,_molecular,_and_optical_physics&action=edit&section=1" title="Edit section: Atomic and molecular physics"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1236090951">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">Main articles: <a href="/wiki/Atomic_physics" title="Atomic physics">Atomic physics</a> and <a href="/wiki/Molecular_physics" title="Molecular physics">Molecular physics</a></div> <p><b>Atomic physics</b> is the subfield of AMO that studies atoms as an isolated system of <a href="/wiki/Electron" title="Electron">electrons</a> and an <a href="/wiki/Atomic_nuclei" class="mw-redirect" title="Atomic nuclei">atomic nucleus</a>, while <b>molecular physics</b> is the study of the physical properties of <a href="/wiki/Molecule" title="Molecule">molecules</a>. The term <i>atomic physics</i> is often associated with <a href="/wiki/Nuclear_power" title="Nuclear power">nuclear power</a> and <a href="/wiki/Nuclear_bomb" class="mw-redirect" title="Nuclear bomb">nuclear bombs</a>, due to the <a href="/wiki/Synonym" title="Synonym">synonymous</a> use of <i>atomic</i> and <i>nuclear</i> in <a href="/wiki/Standard_English" title="Standard English">standard English</a>. However, physicists distinguish between atomic physics — which deals with the atom as a system consisting of a nucleus and electrons — and <a href="/wiki/Nuclear_physics" title="Nuclear physics">nuclear physics</a>, which considers <a href="/wiki/Atomic_nucleus" title="Atomic nucleus">atomic nuclei</a> alone. The important experimental techniques are the various types of <a href="/wiki/Spectroscopy" title="Spectroscopy">spectroscopy</a>. <a href="/wiki/Molecular_physics" title="Molecular physics">Molecular physics</a>, while closely related to <a href="/wiki/Atomic_physics" title="Atomic physics">atomic physics</a>, also overlaps greatly with <a href="/wiki/Theoretical_chemistry" title="Theoretical chemistry">theoretical chemistry</a>, <a href="/wiki/Physical_chemistry" title="Physical chemistry">physical chemistry</a> and <a href="/wiki/Chemical_physics" title="Chemical physics">chemical physics</a>.<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p><p>Both subfields are primarily concerned with <a href="/wiki/Electronic_structure" class="mw-redirect" title="Electronic structure">electronic structure</a> and the dynamical processes by which these arrangements change. Generally this work involves using quantum mechanics. For molecular physics, this approach is known as <a href="/wiki/Quantum_chemistry" title="Quantum chemistry">quantum chemistry</a>. One important aspect of molecular physics is that the essential <a href="/wiki/Atomic_orbital" title="Atomic orbital">atomic orbital</a> theory in the field of atomic physics expands to the <a href="/wiki/Molecular_orbital" title="Molecular orbital">molecular orbital</a> theory.<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> Molecular physics is concerned with atomic processes in molecules, but it is additionally concerned with effects due to the <a href="/wiki/Molecular_structure" class="mw-redirect" title="Molecular structure">molecular structure</a>. Additionally to the electronic excitation states which are known from atoms, molecules are able to rotate and to vibrate. These rotations and vibrations are quantized; there are discrete <a href="/wiki/Energy_level" title="Energy level">energy levels</a>. The smallest energy differences exist between different rotational states, therefore pure rotational <a href="/wiki/Spectrum" title="Spectrum">spectra</a> are in the far <a href="/wiki/Infrared" title="Infrared">infrared</a> region (about 30 - 150 <a href="/wiki/%CE%9Cm" class="mw-redirect" title="Μm">μm</a> <a href="/wiki/Wavelength" title="Wavelength">wavelength</a>) of the <a href="/wiki/Electromagnetic_spectrum" title="Electromagnetic spectrum">electromagnetic spectrum</a>. <a href="/wiki/Vibrational_spectroscopy_of_linear_molecules" title="Vibrational spectroscopy of linear molecules">Vibrational spectra</a> are in the near infrared (about 1 - 5 μm) and spectra resulting from electronic transitions are mostly in the visible and <a href="/wiki/Ultraviolet" title="Ultraviolet">ultraviolet</a> regions. From measuring rotational and vibrational spectra properties of molecules like the distance between the nuclei can be calculated.<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> </p><p>As with many scientific fields, strict delineation can be highly contrived and atomic physics is often considered in the wider context of <i>atomic, molecular, and optical physics</i>. Physics research groups are usually so classified. </p> <div class="mw-heading mw-heading2"><h2 id="Optical_physics">Optical physics</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Atomic,_molecular,_and_optical_physics&action=edit&section=2" title="Edit section: Optical physics"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">See also: <a href="/wiki/Optics" title="Optics">Optics</a></div> <p><b>Optical physics</b> is the study of the generation of <a href="/wiki/Electromagnetic_radiation" title="Electromagnetic radiation">electromagnetic radiation</a>, the properties of that radiation, and the interaction of that radiation with <a href="/wiki/Matter" title="Matter">matter</a>,<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> especially its manipulation and control.<sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> It differs from general <a href="/wiki/Optics" title="Optics">optics</a> and <a href="/wiki/Optical_engineering" title="Optical engineering">optical engineering</a> in that it is focused on the discovery and application of new phenomena. There is no strong distinction, however, between optical physics, applied optics, and optical engineering, since the devices of optical engineering and the applications of applied optics are necessary for basic research in optical physics, and that research leads to the development of new devices and applications. Often the same people are involved in both the basic research and the applied technology development, for example the experimental demonstration of <a href="/wiki/Electromagnetically_induced_transparency" title="Electromagnetically induced transparency">electromagnetically induced transparency</a> by <a href="/wiki/S._E._Harris" class="mw-redirect" title="S. E. Harris">S. E. Harris</a> and of <a href="/wiki/Slow_light" title="Slow light">slow light</a> by Harris and <a href="/wiki/Lene_Vestergaard_Hau" class="mw-redirect" title="Lene Vestergaard Hau">Lene Vestergaard Hau</a>.<sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> </p><p>Researchers in optical physics use and develop light sources that span the <a href="/wiki/Electromagnetic_spectrum" title="Electromagnetic spectrum">electromagnetic spectrum</a> from <a href="/wiki/Microwave" title="Microwave">microwaves</a> to <a href="/wiki/X-ray" title="X-ray">X-rays</a>. The field includes the generation and detection of light, linear and <a href="/wiki/Nonlinear_optics" title="Nonlinear optics">nonlinear</a> optical processes, and <a href="/wiki/Spectroscopy" title="Spectroscopy">spectroscopy</a>. <a href="/wiki/Laser" title="Laser">Lasers</a> and <a href="/wiki/Laser_spectroscopy" class="mw-redirect" title="Laser spectroscopy">laser spectroscopy</a> have transformed optical science. Major study in optical physics is also devoted to <a href="/wiki/Quantum_optics" title="Quantum optics">quantum optics</a> and <a href="/wiki/Coherence_(physics)" title="Coherence (physics)">coherence</a>, and to <a href="/wiki/Femtosecond" title="Femtosecond">femtosecond</a> optics.<sup id="cite_ref-nap_1-1" class="reference"><a href="#cite_note-nap-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> In optical physics, support is also provided in areas such as the nonlinear response of isolated atoms to intense, ultra-short electromagnetic fields, the atom-cavity interaction at high fields, and quantum properties of the electromagnetic field.<sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> </p><p>Other important areas of research include the development of novel optical techniques for nano-optical measurements, <a href="/wiki/Diffractive_optics" class="mw-redirect" title="Diffractive optics">diffractive optics</a>, <a href="/wiki/Interferometry" title="Interferometry">low-coherence interferometry</a>, <a href="/wiki/Optical_coherence_tomography" title="Optical coherence tomography">optical coherence tomography</a>, and <a href="/wiki/Near-field_scanning_optical_microscope" title="Near-field scanning optical microscope">near-field microscopy</a>. Research in optical physics places an emphasis on ultrafast optical science and technology. The applications of optical physics create advancements in <a href="/wiki/Telecommunications" title="Telecommunications">communications</a>, <a href="/wiki/Medicine" title="Medicine">medicine</a>, <a href="/wiki/Manufacturing" title="Manufacturing">manufacturing</a>, and even <a href="/wiki/Entertainment" title="Entertainment">entertainment</a>.<sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="History">History</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Atomic,_molecular,_and_optical_physics&action=edit&section=3" title="Edit section: History"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main articles: <a href="/wiki/Atomic_theory" class="mw-redirect" title="Atomic theory">Atomic theory</a> and <a href="/wiki/Basics_of_quantum_mechanics" class="mw-redirect" title="Basics of quantum mechanics">Basics of quantum mechanics</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>The <a href="/wiki/Bohr_model" title="Bohr model">Bohr model</a> of the <a href="/wiki/Hydrogen_atom" title="Hydrogen atom">Hydrogen atom</a></figcaption></figure> <p>One of the earliest steps towards <i>atomic physics</i> was the recognition that matter was composed of <i>atoms</i>, in modern terms the basic unit of a <a href="/wiki/Chemical_element" title="Chemical element">chemical element</a>. This theory was developed by <a href="/wiki/John_Dalton" title="John Dalton">John Dalton</a> in the 18th century. At this stage, it wasn't clear what atoms were - although they could be described and classified by their observable properties in bulk; summarized by the developing <a href="/wiki/Periodic_table" title="Periodic table">periodic table</a>, by <a href="/wiki/John_Alexander_Reina_Newlands" class="mw-redirect" title="John Alexander Reina Newlands">John Newlands</a> and <a href="/wiki/Dmitri_Mendeleyev" class="mw-redirect" title="Dmitri Mendeleyev">Dmitri Mendeleyev</a> around the mid to late 19th century.<sup id="cite_ref-R.E._Dickerson,_I._Geis_1976_13-0" class="reference"><a href="#cite_note-R.E._Dickerson,_I._Geis_1976-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> </p><p>Later, the connection between atomic physics <i>and</i> optical physics became apparent, by the discovery of <a href="/wiki/Spectral_line" title="Spectral line">spectral lines</a> and attempts to describe the phenomenon - notably by <a href="/wiki/Joseph_von_Fraunhofer" title="Joseph von Fraunhofer">Joseph von Fraunhofer</a>, <a href="/wiki/Fresnel" class="mw-redirect" title="Fresnel">Fresnel</a>, and others in the 19th century.<sup id="cite_ref-14" class="reference"><a href="#cite_note-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> </p><p>From that time to the 1920s, physicists were seeking to explain <a href="/wiki/Atomic_spectra" class="mw-redirect" title="Atomic spectra">atomic spectra</a> and <a href="/wiki/Blackbody_radiation" class="mw-redirect" title="Blackbody radiation">blackbody radiation</a>. One attempt to explain hydrogen spectral lines was the <a href="/wiki/Bohr_atom_model" class="mw-redirect" title="Bohr atom model">Bohr atom model</a>.<sup id="cite_ref-R.E._Dickerson,_I._Geis_1976_13-1" class="reference"><a href="#cite_note-R.E._Dickerson,_I._Geis_1976-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> </p><p>Experiments including <a href="/wiki/Electromagnetic_radiation" title="Electromagnetic radiation">electromagnetic radiation</a> and matter - such as the <a href="/wiki/Photoelectric_effect" title="Photoelectric effect">photoelectric effect</a>, <a href="/wiki/Compton_effect" class="mw-redirect" title="Compton effect">Compton effect</a>, and spectra of sunlight the due to the unknown element of <a href="/wiki/Helium" title="Helium">Helium</a>, the limitation of the Bohr model to Hydrogen, and numerous other reasons, lead to an entirely new mathematical model of matter and light: <a href="/wiki/Quantum_mechanics" title="Quantum mechanics">quantum mechanics</a>.<sup id="cite_ref-15" class="reference"><a href="#cite_note-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Classical_oscillator_model_of_matter">Classical oscillator model of matter</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Atomic,_molecular,_and_optical_physics&action=edit&section=4" title="Edit section: Classical oscillator model of matter"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Early models to explain the origin of the <a href="/wiki/Refractive_index" title="Refractive index">index of refraction</a> treated an <a href="/wiki/Electron" title="Electron">electron</a> in an atomic system classically according to the model of <a href="/wiki/Paul_Drude" title="Paul Drude">Paul Drude</a> and <a href="/wiki/Hendrik_Lorentz" title="Hendrik Lorentz">Hendrik Lorentz</a>. The theory was developed to attempt to provide an origin for the wavelength-dependent refractive index <i>n</i> of a material. In this model, incident <a href="/wiki/Electromagnetic_waves" class="mw-redirect" title="Electromagnetic waves">electromagnetic waves</a> forced an electron bound to an atom to <a href="/wiki/Oscillation" title="Oscillation">oscillate</a>. The <a href="/wiki/Amplitude" title="Amplitude">amplitude</a> of the oscillation would then have a relationship to the <a href="/wiki/Frequency" title="Frequency">frequency</a> of the incident electromagnetic wave and the <a href="/wiki/Resonance" title="Resonance">resonant</a> frequencies of the oscillator. The <a href="/wiki/Superposition_principle" title="Superposition principle">superposition</a> of these emitted waves from many oscillators would then lead to a wave which moved more slowly. <sup id="cite_ref-Haken_16-0" class="reference"><a href="#cite_note-Haken-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 4–8">: 4–8 </span></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Early_quantum_model_of_matter_and_light">Early quantum model of matter and light</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Atomic,_molecular,_and_optical_physics&action=edit&section=5" title="Edit section: Early quantum model of matter and light"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/Max_Planck" title="Max Planck">Max Planck</a> derived a formula to describe the <a href="/wiki/Electromagnetic_field" title="Electromagnetic field">electromagnetic field</a> inside a box when in <a href="/wiki/Thermal_equilibrium" title="Thermal equilibrium">thermal equilibrium</a> in 1900.<sup id="cite_ref-Haken_16-1" class="reference"><a href="#cite_note-Haken-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 8–9">: 8–9 </span></sup> His model consisted of a superposition of <a href="/wiki/Standing_waves" class="mw-redirect" title="Standing waves">standing waves</a>. In one dimension, the box has length <i>L</i>, and only sinusoidal waves of <a href="/wiki/Wavenumber" title="Wavenumber">wavenumber</a> </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle k={\frac {n\pi }{L}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>k</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>n</mi> <mi>π</mi> </mrow> <mi>L</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle k={\frac {n\pi }{L}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/587e5d187030cbcf4199f77390e6edb8c3fafdf2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:7.873ex; height:4.676ex;" alt="{\displaystyle k={\frac {n\pi }{L}}}"></span></dd></dl> <p>can occur in the box, where <i>n</i> is a positive <a href="/wiki/Integer" title="Integer">integer</a> (mathematically denoted by <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \scriptstyle n\in \mathbb {N} _{1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="1"> <mi>n</mi> <mo>∈</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">N</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \scriptstyle n\in \mathbb {N} _{1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7ac9a62f2975c197acae3bb33aa402c69d99fd7d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:4.101ex; height:1.843ex;" alt="{\displaystyle \scriptstyle n\in \mathbb {N} _{1}}"></span>). The equation describing these standing waves is given by: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E=E_{0}\sin \left({\frac {n\pi }{L}}x\right)\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>E</mi> <mo>=</mo> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mi>sin</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>n</mi> <mi>π</mi> </mrow> <mi>L</mi> </mfrac> </mrow> <mi>x</mi> </mrow> <mo>)</mo> </mrow> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E=E_{0}\sin \left({\frac {n\pi }{L}}x\right)\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/547f9912ffff3795eb78284379d04064b6a2f9ec" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; margin-right: -0.387ex; width:18.941ex; height:4.843ex;" alt="{\displaystyle E=E_{0}\sin \left({\frac {n\pi }{L}}x\right)\,\!}"></span>.</dd></dl> <p>where <i>E</i><sub>0</sub> is the magnitude of the <a href="/wiki/Electric_field" title="Electric field">electric field</a> amplitude, and <i>E</i> is the magnitude of the electric field at position <i>x</i>. From this basic, <a href="/wiki/Planck%27s_law" title="Planck's law">Planck's law</a> was derived.<sup id="cite_ref-Haken_16-2" class="reference"><a href="#cite_note-Haken-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 4–8, 51–52">: 4–8, 51–52 </span></sup> </p><p>In 1911, <a href="/wiki/Ernest_Rutherford" title="Ernest Rutherford">Ernest Rutherford</a> concluded, based on alpha particle scattering, that an atom has a central pointlike proton. He also thought that an electron would be still attracted to the proton by Coulomb's law, which he had verified still held at small scales. As a result, he believed that electrons revolved around the proton. <a href="/wiki/Niels_Bohr" title="Niels Bohr">Niels Bohr</a>, in 1913, combined the Rutherford model of the atom with the quantisation ideas of Planck. Only specific and well-defined orbits of the electron could exist, which also do not radiate light. In jumping orbit the electron would emit or absorb light corresponding to the difference in energy of the orbits. His prediction of the energy levels was then consistent with observation.<sup id="cite_ref-Haken_16-3" class="reference"><a href="#cite_note-Haken-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 9–10">: 9–10 </span></sup> </p><p>These results, based on a <i>discrete</i> set of specific standing waves, were inconsistent with the <i>continuous</i> classical oscillator model.<sup id="cite_ref-Haken_16-4" class="reference"><a href="#cite_note-Haken-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 8">: 8 </span></sup> </p><p>Work by <a href="/wiki/Albert_Einstein" title="Albert Einstein">Albert Einstein</a> in 1905 on the <a href="/wiki/Photoelectric_effect" title="Photoelectric effect">photoelectric effect</a> led to the association of a light wave of frequency <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><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></span><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 }"></span> with a photon of energy <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle h\nu }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>h</mi> <mi>ν</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle h\nu }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3cc23768f43b26085f80e1882a94b31d24abd653" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.571ex; height:2.176ex;" alt="{\displaystyle h\nu }"></span>. In 1917 Einstein created an extension to Bohrs model by the introduction of the three processes of <a href="/wiki/Stimulated_emission" title="Stimulated emission">stimulated emission</a>, <a href="/wiki/Spontaneous_emission" title="Spontaneous emission">spontaneous emission</a> and <a href="/wiki/Absorption_(electromagnetic_radiation)" title="Absorption (electromagnetic radiation)">absorption (electromagnetic radiation)</a>.<sup id="cite_ref-Haken_16-5" class="reference"><a href="#cite_note-Haken-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 11">: 11 </span></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Modern_treatments">Modern treatments</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Atomic,_molecular,_and_optical_physics&action=edit&section=6" title="Edit section: Modern treatments"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The largest steps towards the modern treatment was the formulation of quantum mechanics with the <a href="/wiki/Matrix_mechanics" title="Matrix mechanics">matrix mechanics</a> approach by <a href="/wiki/Werner_Heisenberg" title="Werner Heisenberg">Werner Heisenberg</a> and the discovery of the <a href="/wiki/Schr%C3%B6dinger_equation" title="Schrödinger equation">Schrödinger equation</a> by <a href="/wiki/Erwin_Schr%C3%B6dinger" title="Erwin Schrödinger">Erwin Schrödinger</a>.<sup id="cite_ref-Haken_16-6" class="reference"><a href="#cite_note-Haken-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 12">: 12 </span></sup> </p><p>There are a variety of semi-classical treatments within AMO. Which aspects of the problem are treated quantum mechanically and which are treated classically is dependent on the specific problem at hand. The semi-classical approach is ubiquitous in computational work within AMO, largely due to the large decrease in computational cost and complexity associated with it. </p><p>For matter under the action of a laser, a fully quantum mechanical treatment of the atomic or molecular system is combined with the system being under the action of a classical electromagnetic field.<sup id="cite_ref-Haken_16-7" class="reference"><a href="#cite_note-Haken-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 14">: 14 </span></sup> Since the field is treated classically it can not deal with <a href="/wiki/Spontaneous_emission" title="Spontaneous emission">spontaneous emission</a>.<sup id="cite_ref-Haken_16-8" class="reference"><a href="#cite_note-Haken-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 16">: 16 </span></sup> This semi-classical treatment is valid for most systems,<sup id="cite_ref-Drake_2-1" class="reference"><a href="#cite_note-Drake-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 997">: 997 </span></sup> particular those under the action of high intensity laser fields.<sup id="cite_ref-Drake_2-2" class="reference"><a href="#cite_note-Drake-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 724">: 724 </span></sup> The distinction between optical physics and quantum optics is the use of semi-classical and fully quantum treatments respectively.<sup id="cite_ref-Drake_2-3" class="reference"><a href="#cite_note-Drake-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 997">: 997 </span></sup> </p><p>Within collision dynamics and using the semi-classical treatment, the internal degrees of freedom may be treated quantum mechanically, whilst the relative motion of the quantum systems under consideration are treated classically.<sup id="cite_ref-Drake_2-4" class="reference"><a href="#cite_note-Drake-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 556">: 556 </span></sup> When considering medium to high speed collisions, the nuclei can be treated classically while the electron is treated quantum mechanically. In low speed collisions the approximation fails.<sup id="cite_ref-Drake_2-5" class="reference"><a href="#cite_note-Drake-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 754">: 754 </span></sup> </p><p>Classical Monte-Carlo methods for the dynamics of electrons can be described as semi-classical in that the initial conditions are calculated using a fully quantum treatment, but all further treatment is classical.<sup id="cite_ref-Drake_2-6" class="reference"><a href="#cite_note-Drake-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 871">: 871 </span></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Isolated_atoms_and_molecules">Isolated atoms and molecules</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Atomic,_molecular,_and_optical_physics&action=edit&section=7" title="Edit section: Isolated atoms and molecules"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Atomic, Molecular and Optical physics frequently considers atoms and molecules in isolation. Atomic models will consist of a single nucleus that may be surrounded by one or more bound electrons, whilst molecular models are typically concerned with molecular hydrogen and its <a href="/wiki/Molecular_hydrogen_ion" class="mw-redirect" title="Molecular hydrogen ion">molecular hydrogen ion</a>. It is concerned with processes such as <a href="/wiki/Ionization" title="Ionization">ionization</a>, <a href="/wiki/Above_threshold_ionization" class="mw-redirect" title="Above threshold ionization">above threshold ionization</a> and <a href="/wiki/Excited_state" title="Excited state">excitation</a> by photons or collisions with atomic particles. </p><p>While modelling atoms in isolation may not seem realistic, if one considers molecules in a <a href="/wiki/Gas" title="Gas">gas</a> or <a href="/wiki/Plasma_(physics)" title="Plasma (physics)">plasma</a> then the time-scales for molecule-molecule interactions are huge in comparison to the atomic and molecular processes that we are concerned with. This means that the individual molecules can be treated as if each were in isolation for the vast majority of the time. By this consideration atomic and molecular physics provides the underlying theory in <a href="/wiki/Plasma_(physics)" title="Plasma (physics)">plasma physics</a> and <a href="/wiki/Atmospheric_physics" title="Atmospheric physics">atmospheric physics</a> even though both deal with huge numbers of molecules. </p> <div class="mw-heading mw-heading2"><h2 id="Electronic_configuration">Electronic configuration</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Atomic,_molecular,_and_optical_physics&action=edit&section=8" title="Edit section: Electronic configuration"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Electrons form notional <a href="/wiki/Electron_shell" title="Electron shell">shells</a> around the nucleus. These are naturally in a <a href="/wiki/Ground_state" title="Ground state">ground state</a> but can be excited by the absorption of energy from light (<a href="/wiki/Photon" title="Photon">photons</a>), magnetic fields, or interaction with a colliding particle (typically other electrons). </p><p>Electrons that populate a shell are said to be in a <a href="/wiki/Bound_state" title="Bound state">bound state</a>. The energy necessary to remove an electron from its shell (taking it to infinity) is called the <a href="/wiki/Binding_energy" title="Binding energy">binding energy</a>. Any quantity of energy absorbed by the electron in excess of this amount is converted to <a href="/wiki/Kinetic_energy" title="Kinetic energy">kinetic energy</a> according to the <a href="/wiki/Conservation_of_energy" title="Conservation of energy">conservation of energy</a>. The atom is said to have undergone the process of <a href="/wiki/Ionization" title="Ionization">ionization</a>. </p><p>In the event that the electron absorbs a quantity of energy less than the binding energy, it may transition to an <a href="/wiki/Excited_state" title="Excited state">excited state</a> or to a <a href="/wiki/Virtual_state_(physics)" class="mw-redirect" title="Virtual state (physics)">virtual state</a>. After a statistically sufficient quantity of time, an electron in an excited state will undergo a transition to a lower state via <a href="/wiki/Spontaneous_emission" title="Spontaneous emission">spontaneous emission</a>. The change in energy between the two energy levels must be accounted for (conservation of energy). In a neutral atom, the system will emit a photon of the difference in energy. However, if the lower state is in an inner shell, a phenomenon known as the <a href="/wiki/Auger_effect" title="Auger effect">Auger effect</a> may take place where the energy is transferred to another bound electrons causing it to go into the continuum. This allows one to multiply ionize an atom with a single photon. </p><p>There are strict <a href="/wiki/Selection_rules" class="mw-redirect" title="Selection rules">selection rules</a> as to the electronic configurations that can be reached by excitation by light—however there are no such rules for excitation by collision processes. </p> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Atomic,_molecular,_and_optical_physics&action=edit&section=9" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1266661725">.mw-parser-output .portalbox{padding:0;margin:0.5em 0;display:table;box-sizing:border-box;max-width:175px;list-style:none}.mw-parser-output .portalborder{border:1px solid var(--border-color-base,#a2a9b1);padding:0.1em;background:var(--background-color-neutral-subtle,#f8f9fa)}.mw-parser-output .portalbox-entry{display:table-row;font-size:85%;line-height:110%;height:1.9em;font-style:italic;font-weight:bold}.mw-parser-output .portalbox-image{display:table-cell;padding:0.2em;vertical-align:middle;text-align:center}.mw-parser-output .portalbox-link{display:table-cell;padding:0.2em 0.2em 0.2em 0.3em;vertical-align:middle}@media(min-width:720px){.mw-parser-output .portalleft{margin:0.5em 1em 0.5em 0}.mw-parser-output .portalright{clear:right;float:right;margin:0.5em 0 0.5em 1em}}</style><ul role="navigation" aria-label="Portals" class="noprint portalbox portalborder portalright"> <li class="portalbox-entry"><span class="portalbox-image"><span class="noviewer" typeof="mw:File"><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></span></span><span class="portalbox-link"><a href="/wiki/Portal:Physics" title="Portal:Physics">Physics portal</a></span></li></ul> <style data-mw-deduplicate="TemplateStyles:r1184024115">.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}</style><div class="div-col" style="column-width: 20em;"> <ul><li><a href="/wiki/Born%E2%80%93Oppenheimer_approximation" title="Born–Oppenheimer approximation">Born–Oppenheimer approximation</a></li> <li><a href="/wiki/Second-harmonic_generation" title="Second-harmonic generation">Frequency doubling</a></li> <li><a href="/wiki/Diffraction" title="Diffraction">Diffraction</a></li> <li><a href="/wiki/Hyperfine_structure" title="Hyperfine structure">Hyperfine structure</a></li> <li><a href="/wiki/Interferometry" title="Interferometry">Interferometry</a></li> <li><a href="/wiki/Isomeric_shift" title="Isomeric shift">Isomeric shift</a></li> <li><a href="/wiki/Metamaterial_cloaking" title="Metamaterial cloaking">Metamaterial cloaking</a></li> <li><a href="/wiki/Molecular_energy_state" class="mw-redirect" title="Molecular energy state">Molecular energy state</a></li> <li><a href="/wiki/Molecular_modelling" title="Molecular modelling">Molecular modeling</a></li> <li><a href="/wiki/Nanotechnology" title="Nanotechnology">Nanotechnology</a></li> <li><a href="/wiki/Negative_index_metamaterials" class="mw-redirect" title="Negative index metamaterials">Negative index metamaterials</a></li> <li><a href="/wiki/Nonlinear_optics" title="Nonlinear optics">Nonlinear optics</a></li> <li><a href="/wiki/Optical_engineering" title="Optical engineering">Optical engineering</a></li> <li><a href="/wiki/Photon_polarization" title="Photon polarization">Photon polarization</a></li> <li><a href="/wiki/Quantum_chemistry" title="Quantum chemistry">Quantum chemistry</a></li> <li><a href="/wiki/Quantum_optics" title="Quantum optics">Quantum optics</a></li> <li><a href="/wiki/Rigid_rotor" title="Rigid rotor">Rigid rotor</a></li> <li><a href="/wiki/Spectroscopy" title="Spectroscopy">Spectroscopy</a></li> <li><a href="/wiki/Superlens" title="Superlens">Superlens</a></li> <li><a href="/wiki/Stationary_state" title="Stationary state">Stationary state</a></li> <li><a href="/wiki/Transition_of_state" class="mw-redirect" title="Transition of state">Transition of state</a></li></ul> </div> <div class="mw-heading mw-heading2"><h2 id="Notes">Notes</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Atomic,_molecular,_and_optical_physics&action=edit&section=10" title="Edit section: Notes"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> <div class="mw-references-wrap mw-references-columns"><ol class="references"> <li id="cite_note-nap-1"><span class="mw-cite-backlink">^ <a href="#cite_ref-nap_1-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-nap_1-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite class="citation book cs1"><a rel="nofollow" class="external text" href="https://archive.org/details/atomicmolecularo00nati_0"><i>Atomic, molecular, and optical physics</i></a>. National Academy Press. 1986. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-309-03575-0" title="Special:BookSources/978-0-309-03575-0"><bdi>978-0-309-03575-0</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Atomic%2C+molecular%2C+and+optical+physics&rft.pub=National+Academy+Press&rft.date=1986&rft.isbn=978-0-309-03575-0&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fatomicmolecularo00nati_0&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAtomic%2C+molecular%2C+and+optical+physics" class="Z3988"></span></span> </li> <li id="cite_note-Drake-2"><span class="mw-cite-backlink">^ <a href="#cite_ref-Drake_2-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Drake_2-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-Drake_2-2"><sup><i><b>c</b></i></sup></a> <a href="#cite_ref-Drake_2-3"><sup><i><b>d</b></i></sup></a> <a href="#cite_ref-Drake_2-4"><sup><i><b>e</b></i></sup></a> <a href="#cite_ref-Drake_2-5"><sup><i><b>f</b></i></sup></a> <a href="#cite_ref-Drake_2-6"><sup><i><b>g</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGordon_Drake1996" class="citation book cs1">Gordon Drake, ed. (1996). <i>Handbook of atomic, molecular, and optical physics</i>. <a href="/wiki/Springer_Science%2BBusiness_Media" title="Springer Science+Business Media">Springer</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-387-20802-2" title="Special:BookSources/978-0-387-20802-2"><bdi>978-0-387-20802-2</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Handbook+of+atomic%2C+molecular%2C+and+optical+physics&rft.pub=Springer&rft.date=1996&rft.isbn=978-0-387-20802-2&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAtomic%2C+molecular%2C+and+optical+physics" class="Z3988"></span></span> </li> <li id="cite_note-chen-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-chen_3-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFChen2009" class="citation book cs1">Chen, L. T., ed. (2009). <i>Atomic, Molecular and Optical Physics: New Research</i>. Nova Science Publishers. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-60456-907-0" title="Special:BookSources/978-1-60456-907-0"><bdi>978-1-60456-907-0</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Atomic%2C+Molecular+and+Optical+Physics%3A+New+Research&rft.pub=Nova+Science+Publishers&rft.date=2009&rft.isbn=978-1-60456-907-0&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAtomic%2C+molecular%2C+and+optical+physics" class="Z3988"></span></span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFC.B._Parker1994" class="citation book cs1">C.B. Parker (1994). <a rel="nofollow" class="external text" href="https://archive.org/details/mcgrawhillencycl1993park/page/803"><i>McGraw Hill Encyclopaedia of Physics</i></a> (2nd ed.). McGraw Hill. p. <a rel="nofollow" class="external text" href="https://archive.org/details/mcgrawhillencycl1993park/page/803">803</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-07-051400-3" title="Special:BookSources/978-0-07-051400-3"><bdi>978-0-07-051400-3</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=McGraw+Hill+Encyclopaedia+of+Physics&rft.pages=803&rft.edition=2nd&rft.pub=McGraw+Hill&rft.date=1994&rft.isbn=978-0-07-051400-3&rft.au=C.B.+Parker&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fmcgrawhillencycl1993park%2Fpage%2F803&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAtomic%2C+molecular%2C+and+optical+physics" class="Z3988"></span></span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-5">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFR._E._DickersonI._Geis1976" class="citation book cs1">R. E. Dickerson; I. Geis (1976). "chapter 9". <i>Chemistry, Matter, and the Universe</i>. W.A. Benjamin Inc. (USA). <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-19-855148-5" title="Special:BookSources/978-0-19-855148-5"><bdi>978-0-19-855148-5</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=chapter+9&rft.btitle=Chemistry%2C+Matter%2C+and+the+Universe&rft.pub=W.A.+Benjamin+Inc.+%28USA%29&rft.date=1976&rft.isbn=978-0-19-855148-5&rft.au=R.+E.+Dickerson&rft.au=I.+Geis&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAtomic%2C+molecular%2C+and+optical+physics" class="Z3988"></span></span> </li> <li id="cite_note-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-6">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFI.R._Kenyon2008" class="citation book cs1">I.R. Kenyon (2008). <span class="id-lock-registration" title="Free registration required"><a rel="nofollow" class="external text" href="https://archive.org/details/lightfantasticmo0000keny">"chapters 12, 13, 17"</a></span>. <i>The Light Fantastic – Introduction to Classic and Quantum Optics</i>. Oxford University Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-19-856646-5" title="Special:BookSources/978-0-19-856646-5"><bdi>978-0-19-856646-5</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=chapters+12%2C+13%2C+17&rft.btitle=The+Light+Fantastic+%E2%80%93+Introduction+to+Classic+and+Quantum+Optics&rft.pub=Oxford+University+Press&rft.date=2008&rft.isbn=978-0-19-856646-5&rft.au=I.R.+Kenyon&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Flightfantasticmo0000keny&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAtomic%2C+molecular%2C+and+optical+physics" class="Z3988"></span></span> </li> <li id="cite_note-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-7">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFY._B._Band2010" class="citation book cs1">Y. B. Band (2010). "chapters 3". <i>Light and Matter: Electromagnetism, Optics, Spectroscopy and Lasers</i>. John Wiley & Sons. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-471-89931-0" title="Special:BookSources/978-0-471-89931-0"><bdi>978-0-471-89931-0</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=chapters+3&rft.btitle=Light+and+Matter%3A+Electromagnetism%2C+Optics%2C+Spectroscopy+and+Lasers&rft.pub=John+Wiley+%26+Sons&rft.date=2010&rft.isbn=978-0-471-89931-0&rft.au=Y.+B.+Band&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAtomic%2C+molecular%2C+and+optical+physics" class="Z3988"></span></span> </li> <li id="cite_note-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-8">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20190513183339/http://www.optics.arizona.edu/research/faculty-specialties/optical-physics">"Optical Physics"</a>. University of Arizona. Archived from <a rel="nofollow" class="external text" href="http://www.optics.arizona.edu/research/faculty-specialties/optical-physics">the original</a> on May 13, 2019<span class="reference-accessdate">. Retrieved <span class="nowrap">Apr 23,</span> 2014</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Optical+Physics&rft.pub=University+of+Arizona&rft_id=http%3A%2F%2Fwww.optics.arizona.edu%2Fresearch%2Ffaculty-specialties%2Foptical-physics&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAtomic%2C+molecular%2C+and+optical+physics" class="Z3988"></span></span> </li> <li id="cite_note-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-9">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://sciencewatch.com/nobel/predictions/slow-light">"Slow Light"</a>. <i>Science Watch</i><span class="reference-accessdate">. Retrieved <span class="nowrap">Jan 22,</span> 2013</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Science+Watch&rft.atitle=Slow+Light&rft_id=http%3A%2F%2Fsciencewatch.com%2Fnobel%2Fpredictions%2Fslow-light&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAtomic%2C+molecular%2C+and+optical+physics" class="Z3988"></span></span> </li> <li id="cite_note-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-10">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFY.B._Band2010" class="citation book cs1">Y.B. Band (2010). "chapters 9,10". <i>Light and Matter: Electromagnetism, Optics, Spectroscopy and Lasers</i>. John Wiley & Sons. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-471-89931-0" title="Special:BookSources/978-0-471-89931-0"><bdi>978-0-471-89931-0</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=chapters+9%2C10&rft.btitle=Light+and+Matter%3A+Electromagnetism%2C+Optics%2C+Spectroscopy+and+Lasers&rft.pub=John+Wiley+%26+Sons&rft.date=2010&rft.isbn=978-0-471-89931-0&rft.au=Y.B.+Band&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAtomic%2C+molecular%2C+and+optical+physics" class="Z3988"></span></span> </li> <li id="cite_note-11"><span class="mw-cite-backlink"><b><a href="#cite_ref-11">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFC.B._Parker1994" class="citation book cs1">C.B. Parker (1994). <a rel="nofollow" class="external text" href="https://archive.org/details/mcgrawhillencycl1993park/page/933"><i>McGraw Hill Encyclopaedia of Physics</i></a> (2nd ed.). McGraw Hill. pp. <a rel="nofollow" class="external text" href="https://archive.org/details/mcgrawhillencycl1993park/page/933">933–934</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-07-051400-3" title="Special:BookSources/978-0-07-051400-3"><bdi>978-0-07-051400-3</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=McGraw+Hill+Encyclopaedia+of+Physics&rft.pages=933-934&rft.edition=2nd&rft.pub=McGraw+Hill&rft.date=1994&rft.isbn=978-0-07-051400-3&rft.au=C.B.+Parker&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fmcgrawhillencycl1993park%2Fpage%2F933&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAtomic%2C+molecular%2C+and+optical+physics" class="Z3988"></span></span> </li> <li id="cite_note-12"><span class="mw-cite-backlink"><b><a href="#cite_ref-12">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFI._R._Kenyon2008" class="citation book cs1">I. R. Kenyon (2008). <span class="id-lock-registration" title="Free registration required"><a rel="nofollow" class="external text" href="https://archive.org/details/lightfantasticmo0000keny">"5, 6, 10, 16"</a></span>. <i>The Light Fantastic – Introduction to Classic and Quantum Optics</i> (2nd ed.). Oxford University Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-19-856646-5" title="Special:BookSources/978-0-19-856646-5"><bdi>978-0-19-856646-5</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=5%2C+6%2C+10%2C+16&rft.btitle=The+Light+Fantastic+%E2%80%93+Introduction+to+Classic+and+Quantum+Optics&rft.edition=2nd&rft.pub=Oxford+University+Press&rft.date=2008&rft.isbn=978-0-19-856646-5&rft.au=I.+R.+Kenyon&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Flightfantasticmo0000keny&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAtomic%2C+molecular%2C+and+optical+physics" class="Z3988"></span></span> </li> <li id="cite_note-R.E._Dickerson,_I._Geis_1976-13"><span class="mw-cite-backlink">^ <a href="#cite_ref-R.E._Dickerson,_I._Geis_1976_13-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-R.E._Dickerson,_I._Geis_1976_13-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFR._E._DickersonI._Geis1976" class="citation book cs1">R. E. Dickerson; I. Geis (1976). "chapters 7, 8". <i>Chemistry, Matter, and the Universe</i>. W.A. Benjamin Inc. (USA). <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-19-855148-5" title="Special:BookSources/978-0-19-855148-5"><bdi>978-0-19-855148-5</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=chapters+7%2C+8&rft.btitle=Chemistry%2C+Matter%2C+and+the+Universe&rft.pub=W.A.+Benjamin+Inc.+%28USA%29&rft.date=1976&rft.isbn=978-0-19-855148-5&rft.au=R.+E.+Dickerson&rft.au=I.+Geis&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAtomic%2C+molecular%2C+and+optical+physics" class="Z3988"></span></span> </li> <li id="cite_note-14"><span class="mw-cite-backlink"><b><a href="#cite_ref-14">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFY.B._Band2010" class="citation book cs1">Y.B. Band (2010). <i>Light and Matter: Electromagnetism, Optics, Spectroscopy and Lasers</i>. John Wiley & Sons. pp. <span class="nowrap">4–</span>11. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-471-89931-0" title="Special:BookSources/978-0-471-89931-0"><bdi>978-0-471-89931-0</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Light+and+Matter%3A+Electromagnetism%2C+Optics%2C+Spectroscopy+and+Lasers&rft.pages=%3Cspan+class%3D%22nowrap%22%3E4-%3C%2Fspan%3E11&rft.pub=John+Wiley+%26+Sons&rft.date=2010&rft.isbn=978-0-471-89931-0&rft.au=Y.B.+Band&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAtomic%2C+molecular%2C+and+optical+physics" class="Z3988"></span></span> </li> <li id="cite_note-15"><span class="mw-cite-backlink"><b><a href="#cite_ref-15">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFP._A._TiplerG._Mosca2008" class="citation book cs1">P. A. Tipler; G. Mosca (2008). "chapter 34". <i>Physics for Scientists and Engineers - with Modern Physics</i>. Freeman. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-7167-8964-2" title="Special:BookSources/978-0-7167-8964-2"><bdi>978-0-7167-8964-2</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=chapter+34&rft.btitle=Physics+for+Scientists+and+Engineers+-+with+Modern+Physics&rft.pub=Freeman&rft.date=2008&rft.isbn=978-0-7167-8964-2&rft.au=P.+A.+Tipler&rft.au=G.+Mosca&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAtomic%2C+molecular%2C+and+optical+physics" class="Z3988"></span></span> </li> <li id="cite_note-Haken-16"><span class="mw-cite-backlink">^ <a href="#cite_ref-Haken_16-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Haken_16-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-Haken_16-2"><sup><i><b>c</b></i></sup></a> <a href="#cite_ref-Haken_16-3"><sup><i><b>d</b></i></sup></a> <a href="#cite_ref-Haken_16-4"><sup><i><b>e</b></i></sup></a> <a href="#cite_ref-Haken_16-5"><sup><i><b>f</b></i></sup></a> <a href="#cite_ref-Haken_16-6"><sup><i><b>g</b></i></sup></a> <a href="#cite_ref-Haken_16-7"><sup><i><b>h</b></i></sup></a> <a href="#cite_ref-Haken_16-8"><sup><i><b>i</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHaken1981" class="citation book cs1">Haken, H. (1981). <i>Light</i> (Reprint. ed.). Amsterdam u.a.: North-Holland Physics Publ. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-444-86020-0" title="Special:BookSources/978-0-444-86020-0"><bdi>978-0-444-86020-0</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Light&rft.place=Amsterdam+u.a.&rft.edition=Reprint.&rft.pub=North-Holland+Physics+Publ.&rft.date=1981&rft.isbn=978-0-444-86020-0&rft.aulast=Haken&rft.aufirst=H.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAtomic%2C+molecular%2C+and+optical+physics" class="Z3988"></span></span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Atomic,_molecular,_and_optical_physics&action=edit&section=11" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239549316">.mw-parser-output .refbegin{margin-bottom:0.5em}.mw-parser-output .refbegin-hanging-indents>ul{margin-left:0}.mw-parser-output .refbegin-hanging-indents>ul>li{margin-left:0;padding-left:3.2em;text-indent:-3.2em}.mw-parser-output .refbegin-hanging-indents ul,.mw-parser-output .refbegin-hanging-indents ul li{list-style:none}@media(max-width:720px){.mw-parser-output .refbegin-hanging-indents>ul>li{padding-left:1.6em;text-indent:-1.6em}}.mw-parser-output .refbegin-columns{margin-top:0.3em}.mw-parser-output .refbegin-columns ul{margin-top:0}.mw-parser-output .refbegin-columns li{page-break-inside:avoid;break-inside:avoid-column}@media screen{.mw-parser-output .refbegin{font-size:90%}}</style><div class="refbegin" style=""> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBransden,_B._H.Joachain,_CJ2002" class="citation book cs1">Bransden, B. H.; Joachain, CJ (2002). <i>Physics of Atoms and Molecules</i> (2nd ed.). Prentice Hall. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-582-35692-4" title="Special:BookSources/978-0-582-35692-4"><bdi>978-0-582-35692-4</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Physics+of+Atoms+and+Molecules&rft.edition=2nd&rft.pub=Prentice+Hall&rft.date=2002&rft.isbn=978-0-582-35692-4&rft.au=Bransden%2C+B.+H.&rft.au=Joachain%2C+CJ&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAtomic%2C+molecular%2C+and+optical+physics" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFFoot,_C._J.2004" class="citation book cs1">Foot, C. J. (2004). <i>Atomic Physics</i>. Oxford University Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-19-850696-6" title="Special:BookSources/978-0-19-850696-6"><bdi>978-0-19-850696-6</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Atomic+Physics&rft.pub=Oxford+University+Press&rft.date=2004&rft.isbn=978-0-19-850696-6&rft.au=Foot%2C+C.+J.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAtomic%2C+molecular%2C+and+optical+physics" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHerzberg,_G.1979" class="citation book cs1">Herzberg, G. (1979) [1945]. <i>Atomic Spectra and Atomic Structure</i>. Dover. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-486-60115-1" title="Special:BookSources/978-0-486-60115-1"><bdi>978-0-486-60115-1</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Atomic+Spectra+and+Atomic+Structure&rft.pub=Dover&rft.date=1979&rft.isbn=978-0-486-60115-1&rft.au=Herzberg%2C+G.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAtomic%2C+molecular%2C+and+optical+physics" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFCondon,_E._U.Shortley,_G._H.1935" class="citation book cs1">Condon, E. U. & Shortley, G. H. (1935). <i>The Theory of Atomic Spectra</i>. Cambridge University Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-521-09209-8" title="Special:BookSources/978-0-521-09209-8"><bdi>978-0-521-09209-8</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Theory+of+Atomic+Spectra&rft.pub=Cambridge+University+Press&rft.date=1935&rft.isbn=978-0-521-09209-8&rft.au=Condon%2C+E.+U.&rft.au=Shortley%2C+G.+H.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAtomic%2C+molecular%2C+and+optical+physics" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFCowan,_Robert_D.1981" class="citation book cs1">Cowan, Robert D. (1981). <i>The Theory of Atomic Structure and Spectra</i>. University of California Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-520-03821-9" title="Special:BookSources/978-0-520-03821-9"><bdi>978-0-520-03821-9</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Theory+of+Atomic+Structure+and+Spectra&rft.pub=University+of+California+Press&rft.date=1981&rft.isbn=978-0-520-03821-9&rft.au=Cowan%2C+Robert+D.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAtomic%2C+molecular%2C+and+optical+physics" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLindgren,_I.Morrison,_J.1986" class="citation book cs1">Lindgren, I. & Morrison, J. (1986). <i>Atomic Many-Body Theory</i> (Second ed.). Springer-Verlag. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-387-16649-0" title="Special:BookSources/978-0-387-16649-0"><bdi>978-0-387-16649-0</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Atomic+Many-Body+Theory&rft.edition=Second&rft.pub=Springer-Verlag&rft.date=1986&rft.isbn=978-0-387-16649-0&rft.au=Lindgren%2C+I.&rft.au=Morrison%2C+J.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAtomic%2C+molecular%2C+and+optical+physics" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFJ._R._HookH._E._Hall2010" class="citation book cs1">J. R. Hook; H. E. Hall (2010). <span class="id-lock-registration" title="Free registration required"><a rel="nofollow" class="external text" href="https://archive.org/details/candidevo00volt"><i>Solid State Physics</i></a></span> (2nd ed.). Manchester Physics Series, John Wiley & Sons. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-471-92804-1" title="Special:BookSources/978-0-471-92804-1"><bdi>978-0-471-92804-1</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Solid+State+Physics&rft.edition=2nd&rft.pub=Manchester+Physics+Series%2C+John+Wiley+%26+Sons&rft.date=2010&rft.isbn=978-0-471-92804-1&rft.au=J.+R.+Hook&rft.au=H.+E.+Hall&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fcandidevo00volt&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAtomic%2C+molecular%2C+and+optical+physics" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFP._W._Atkins1978" class="citation book cs1">P. W. Atkins (1978). <i>Physical chemistry</i>. Oxford University Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-19-855148-5" title="Special:BookSources/978-0-19-855148-5"><bdi>978-0-19-855148-5</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Physical+chemistry&rft.pub=Oxford+University+Press&rft.date=1978&rft.isbn=978-0-19-855148-5&rft.au=P.+W.+Atkins&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAtomic%2C+molecular%2C+and+optical+physics" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFY._B._Band2010" class="citation book cs1">Y. B. Band (2010). <i>Light and Matter: Electromagnetism, Optics, Spectroscopy and Lasers</i>. John Wiley & Sons. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-471-89931-0" title="Special:BookSources/978-0-471-89931-0"><bdi>978-0-471-89931-0</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Light+and+Matter%3A+Electromagnetism%2C+Optics%2C+Spectroscopy+and+Lasers&rft.pub=John+Wiley+%26+Sons&rft.date=2010&rft.isbn=978-0-471-89931-0&rft.au=Y.+B.+Band&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAtomic%2C+molecular%2C+and+optical+physics" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFI._R._Kenyon2008" class="citation book cs1">I. R. Kenyon (2008). <span class="id-lock-registration" title="Free registration required"><a rel="nofollow" class="external text" href="https://archive.org/details/lightfantasticmo0000keny"><i>The Light Fantastic – Introduction to Classic and Quantum Optics</i></a></span>. Oxford University Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-19-856646-5" title="Special:BookSources/978-0-19-856646-5"><bdi>978-0-19-856646-5</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Light+Fantastic+%E2%80%93+Introduction+to+Classic+and+Quantum+Optics&rft.pub=Oxford+University+Press&rft.date=2008&rft.isbn=978-0-19-856646-5&rft.au=I.+R.+Kenyon&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Flightfantasticmo0000keny&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAtomic%2C+molecular%2C+and+optical+physics" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFT.Hey,_P.Walters2009" class="citation book cs1">T.Hey, P.Walters (2009). <i>The New Quantum Universe</i>. Cambridge University Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-521-56457-1" title="Special:BookSources/978-0-521-56457-1"><bdi>978-0-521-56457-1</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+New+Quantum+Universe&rft.pub=Cambridge+University+Press&rft.date=2009&rft.isbn=978-0-521-56457-1&rft.au=T.Hey%2C+P.Walters&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAtomic%2C+molecular%2C+and+optical+physics" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFR._Loudon1996" class="citation book cs1">R. Loudon (1996). <i>The Quantum Theory of Light</i>. Oxford University Press (Oxford Science Publications). <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-19-850177-0" title="Special:BookSources/978-0-19-850177-0"><bdi>978-0-19-850177-0</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Quantum+Theory+of+Light&rft.pub=Oxford+University+Press+%28Oxford+Science+Publications%29&rft.date=1996&rft.isbn=978-0-19-850177-0&rft.au=R.+Loudon&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAtomic%2C+molecular%2C+and+optical+physics" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFR._EisbergR._Resnick1985" class="citation book cs1">R. Eisberg; R. Resnick (1985). <a rel="nofollow" class="external text" href="https://archive.org/details/quantumphysicsof00eisb"><i>Quantum Physics of Atoms, Molecules, Solids, Nuclei, and Particles</i></a> (2nd ed.). John Wiley & Sons. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-471-87373-0" title="Special:BookSources/978-0-471-87373-0"><bdi>978-0-471-87373-0</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Quantum+Physics+of+Atoms%2C+Molecules%2C+Solids%2C+Nuclei%2C+and+Particles&rft.edition=2nd&rft.pub=John+Wiley+%26+Sons&rft.date=1985&rft.isbn=978-0-471-87373-0&rft.au=R.+Eisberg&rft.au=R.+Resnick&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fquantumphysicsof00eisb&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAtomic%2C+molecular%2C+and+optical+physics" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFP.W._Atkins1974" class="citation book cs1">P.W. Atkins (1974). <i>Quanta: A handbook of concepts</i>. Oxford University Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-19-855493-6" title="Special:BookSources/978-0-19-855493-6"><bdi>978-0-19-855493-6</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Quanta%3A+A+handbook+of+concepts&rft.pub=Oxford+University+Press&rft.date=1974&rft.isbn=978-0-19-855493-6&rft.au=P.W.+Atkins&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAtomic%2C+molecular%2C+and+optical+physics" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFE._Abers2004" class="citation book cs1">E. Abers (2004). <i>Quantum Mechanics</i>. Pearson Ed., Addison Wesley, Prentice Hall Inc. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-13-146100-0" title="Special:BookSources/978-0-13-146100-0"><bdi>978-0-13-146100-0</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Quantum+Mechanics&rft.pub=Pearson+Ed.%2C+Addison+Wesley%2C+Prentice+Hall+Inc&rft.date=2004&rft.isbn=978-0-13-146100-0&rft.au=E.+Abers&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAtomic%2C+molecular%2C+and+optical+physics" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFP.W._Atkins1977" class="citation book cs1">P.W. Atkins (1977). <i>Molecular Quantum Mechanics Parts I and II: An Introduction to QUANTUM CHEMISTRY (Volume 1)</i>. Oxford University Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-19-855129-4" title="Special:BookSources/978-0-19-855129-4"><bdi>978-0-19-855129-4</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Molecular+Quantum+Mechanics+Parts+I+and+II%3A+An+Introduction+to+QUANTUM+CHEMISTRY+%28Volume+1%29&rft.pub=Oxford+University+Press&rft.date=1977&rft.isbn=978-0-19-855129-4&rft.au=P.W.+Atkins&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAtomic%2C+molecular%2C+and+optical+physics" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFP.W._Atkins1977" class="citation book cs1">P.W. Atkins (1977). <i>Molecular Quantum Mechanics Part III: An Introduction to QUANTUM CHEMISTRY (Volume 2)</i>. Oxford University Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-19-855129-4" title="Special:BookSources/978-0-19-855129-4"><bdi>978-0-19-855129-4</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Molecular+Quantum+Mechanics+Part+III%3A+An+Introduction+to+QUANTUM+CHEMISTRY+%28Volume+2%29&rft.pub=Oxford+University+Press&rft.date=1977&rft.isbn=978-0-19-855129-4&rft.au=P.W.+Atkins&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAtomic%2C+molecular%2C+and+optical+physics" class="Z3988"></span></li> <li><i>Solid State Physics (2nd Edition)</i>, J.R. Hook, H.E. Hall, Manchester Physics Series, John Wiley & Sons, 2010, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978%2B0%2B471%2B92804%2B1" title="Special:BookSources/978+0+471+92804+1">978 0 471 92804 1</a></li> <li><i>Light and Matter: Electromagnetism, Optics, Spectroscopy and Lasers</i>, Y.B. Band, John Wiley & Sons, 2010, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0471-89931-0" title="Special:BookSources/978-0471-89931-0">978-0471-89931-0</a></li> <li><i>The Light Fantastic – Introduction to Classic and Quantum Optics</i>, I.R. Kenyon, Oxford University Press, 2008, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-19-856646-5" title="Special:BookSources/978-0-19-856646-5">978-0-19-856646-5</a></li> <li><i>Handbook of atomic, molecular, and optical physics</i>, Editor: Gordon Drake, <a href="/wiki/Springer_Science%2BBusiness_Media" title="Springer Science+Business Media">Springer</a>, Various authors, 1996, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-387-20802-X" title="Special:BookSources/0-387-20802-X">0-387-20802-X</a></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFFox2010" class="citation book cs1">Fox, Mark (2010). <i>Optical properties of solids</i>. Oxford New York: Oxford University Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-19-957336-3" title="Special:BookSources/978-0-19-957336-3"><bdi>978-0-19-957336-3</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Optical+properties+of+solids&rft.place=Oxford+New+York&rft.pub=Oxford+University+Press&rft.date=2010&rft.isbn=978-0-19-957336-3&rft.aulast=Fox&rft.aufirst=Mark&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAtomic%2C+molecular%2C+and+optical+physics" class="Z3988"></span></li></ul> </div> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Atomic,_molecular,_and_optical_physics&action=edit&section=12" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1235681985">.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:var(--background-color-interactive-subtle,#f8f9fa);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;min-width:0}}@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><style data-mw-deduplicate="TemplateStyles:r1237033735">@media print{body.ns-0 .mw-parser-output .sistersitebox{display:none!important}}@media screen{html.skin-theme-clientpref-night .mw-parser-output .sistersitebox img[src*="Wiktionary-logo-en-v2.svg"]{background-color:white}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .sistersitebox img[src*="Wiktionary-logo-en-v2.svg"]{background-color:white}}</style><div class="side-box side-box-right plainlinks sistersitebox"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1126788409"> <div class="side-box-flex"> <div class="side-box-image"><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Commons-logo.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/30px-Commons-logo.svg.png" decoding="async" width="30" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/45px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/59px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></a></span></div> <div class="side-box-text plainlist">Wikimedia Commons has media related to <span style="font-weight: bold; font-style: italic;"><a href="https://commons.wikimedia.org/wiki/Category:Atomic,_molecular,_and_optical_physics" class="extiw" title="commons:Category:Atomic, molecular, and optical physics">Atomic, molecular, and optical physics</a></span>.</div></div> </div> <ul><li><a rel="nofollow" class="external text" href="http://www.sciencedirect.com/science/bookseries/1049250X">ScienceDirect - Advances In Atomic, Molecular, and Optical Physics</a></li> <li><a rel="nofollow" class="external text" href="http://iopscience.iop.org/0953-4075/">Journal of Physics B: Atomic, Molecular and Optical Physics</a></li></ul> <div class="mw-heading mw-heading3"><h3 id="Institutions">Institutions</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Atomic,_molecular,_and_optical_physics&action=edit&section=13" title="Edit section: Institutions"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a rel="nofollow" class="external text" href="http://www.aps.org/units/damop/">American Physical Society - Division of Atomic, Molecular & Optical Physics</a></li> <li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20090927053332/http://ampd.epsdivisions.org/">European Physical Society - Atomic, Molecular & Optical Physics Division</a></li> <li><a rel="nofollow" class="external text" href="https://www.nsf.gov/funding/pgm_summ.jsp?pims_id=13622">National Science Foundation - Atomic, Molecular and Optical Physics</a></li> <li><a rel="nofollow" class="external text" href="http://cuaweb.mit.edu/">MIT-Harvard Center for Ultracold Atoms</a></li> <li><a rel="nofollow" class="external text" href="https://qfarm.stanford.edu">Stanford QFARM Initiative for Quantum Science & Enginneering</a></li> <li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20190101155151/http://jila.colorado.edu/research/atomic-molecular-physics/atomic-molecular-physics">JILA - Atomic and Molecular Physics</a></li> <li><a rel="nofollow" class="external text" href="http://jqi.umd.edu/">Joint Quantum Institute at University of Maryland and NIST</a></li> <li><a rel="nofollow" class="external text" href="http://www.phy.ornl.gov/">ORNL Physics Division</a></li> <li><a rel="nofollow" class="external text" href="http://web.am.qub.ac.uk/ctamop/">Queen's University Belfast - Center for Theoretical, Atomic, Molecular and Optical Physics</a>,</li> <li><a rel="nofollow" class="external text" href="http://physics.berkeley.edu/research/atomic-molecular-and-optical-physics">University of California, Berkeley - Atomic, Molecular and Optical Physics</a></li></ul> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><style data-mw-deduplicate="TemplateStyles:r1236075235">.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{padding:0.25em 1em;line-height:1.5em;text-align:center}.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{line-height:1.5em;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}.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}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="Major_branches_of_physics48" style="padding:3px"><table class="nowraplinks mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Branches_of_physics" title="Template:Branches of physics"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Branches_of_physics" title="Template talk:Branches of physics"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Branches_of_physics" title="Special:EditPage/Template:Branches of physics"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Major_branches_of_physics48" style="font-size:114%;margin:0 4em">Major <a href="/wiki/Branches_of_physics" title="Branches of physics">branches of physics</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">Divisions</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Basic_research" title="Basic research">Pure</a></li> <li><a href="/wiki/Applied_physics" title="Applied physics">Applied</a> <ul><li><a href="/wiki/Engineering_physics" title="Engineering physics">Engineering</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Approaches</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Experimental_physics" title="Experimental physics">Experimental</a></li> <li><a href="/wiki/Theoretical_physics" title="Theoretical physics">Theoretical</a> <ul><li><a href="/wiki/Computational_physics" title="Computational physics">Computational</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Classical_physics" title="Classical physics">Classical</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Classical_mechanics" title="Classical mechanics">Classical mechanics</a> <ul><li><a href="/wiki/Newton%27s_laws_of_motion" title="Newton's laws of motion">Newtonian</a></li> <li><a href="/wiki/Analytical_mechanics" title="Analytical mechanics">Analytical</a></li> <li><a href="/wiki/Celestial_mechanics" title="Celestial mechanics">Celestial</a></li> <li><a href="/wiki/Continuum_mechanics" title="Continuum mechanics">Continuum</a></li></ul></li> <li><a href="/wiki/Acoustics" title="Acoustics">Acoustics</a></li> <li><a href="/wiki/Classical_electromagnetism" title="Classical electromagnetism">Classical electromagnetism</a></li> <li><a href="/wiki/Classical_optics" class="mw-redirect" title="Classical optics">Classical optics</a> <ul><li><a href="/wiki/Geometrical_optics" title="Geometrical optics">Ray</a></li> <li><a href="/wiki/Physical_optics" title="Physical optics">Wave</a></li></ul></li> <li><a href="/wiki/Thermodynamics" title="Thermodynamics">Thermodynamics</a> <ul><li><a href="/wiki/Statistical_mechanics" title="Statistical mechanics">Statistical</a></li> <li><a href="/wiki/Non-equilibrium_thermodynamics" title="Non-equilibrium thermodynamics">Non-equilibrium</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Modern_physics" title="Modern physics">Modern</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Relativistic_mechanics" title="Relativistic mechanics">Relativistic mechanics</a> <ul><li><a href="/wiki/Special_relativity" title="Special relativity">Special</a></li> <li><a href="/wiki/General_relativity" title="General relativity">General</a></li></ul></li> <li><a href="/wiki/Nuclear_physics" title="Nuclear physics">Nuclear physics</a></li> <li><a href="/wiki/Particle_physics" title="Particle physics">Particle physics</a></li> <li><a href="/wiki/Quantum_mechanics" title="Quantum mechanics">Quantum mechanics</a></li> <li><a class="mw-selflink selflink">Atomic, molecular, and optical physics</a> <ul><li><a href="/wiki/Atomic_physics" title="Atomic physics">Atomic</a></li> <li><a href="/wiki/Molecular_physics" title="Molecular physics">Molecular</a></li> <li><a href="/wiki/Optics#Modern_optics" title="Optics">Modern optics</a></li></ul></li> <li><a href="/wiki/Condensed_matter_physics" title="Condensed matter physics">Condensed matter physics</a> <ul><li><a href="/wiki/Solid-state_physics" title="Solid-state physics">Solid-state physics</a></li> <li><a href="/wiki/Crystallography" title="Crystallography">Crystallography</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Category:Applied_and_interdisciplinary_physics" title="Category:Applied and interdisciplinary physics">Interdisciplinary</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Astrophysics" title="Astrophysics">Astrophysics</a></li> <li><a href="/wiki/Atmospheric_physics" title="Atmospheric physics">Atmospheric physics</a></li> <li><a href="/wiki/Biophysics" title="Biophysics">Biophysics</a></li> <li><a href="/wiki/Chemical_physics" title="Chemical physics">Chemical physics</a></li> <li><a href="/wiki/Geophysics" title="Geophysics">Geophysics</a></li> <li><a href="/wiki/Materials_science" title="Materials science">Materials science</a></li> <li><a href="/wiki/Mathematical_physics" title="Mathematical physics">Mathematical physics</a></li> <li><a href="/wiki/Medical_physics" title="Medical physics">Medical physics</a></li> <li><a href="/wiki/Physical_oceanography" title="Physical oceanography">Ocean physics</a></li> <li><a href="/wiki/Quantum_information_science" title="Quantum information science">Quantum information science</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Related</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/History_of_physics" title="History of physics">History of physics</a></li> <li><a href="/wiki/Nobel_Prize_in_Physics" title="Nobel Prize in Physics">Nobel Prize in Physics</a></li> <li><a href="/wiki/Philosophy_of_physics" title="Philosophy of physics">Philosophy of physics</a></li> <li><a href="/wiki/Physics_education" title="Physics education">Physics education</a> <ul><li><a href="/wiki/Physics_education_research" title="Physics education research">research</a></li></ul></li> <li><a href="/wiki/Timeline_of_fundamental_physics_discoveries" title="Timeline of fundamental physics discoveries">Timeline of physics discoveries</a></li></ul> </div></td></tr></tbody></table></div>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?useformat=desktop&type=1x1&usesul3=0" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Retrieved from "<a dir="ltr" href="https://en.wikipedia.org/w/index.php?title=Atomic,_molecular,_and_optical_physics&oldid=1245940912">https://en.wikipedia.org/w/index.php?title=Atomic,_molecular,_and_optical_physics&oldid=1245940912</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Help:Category" title="Help:Category">Category</a>: <ul><li><a href="/wiki/Category:Atomic,_molecular,_and_optical_physics" title="Category:Atomic, molecular, and optical physics">Atomic, molecular, and optical physics</a></li></ul></div><div id="mw-hidden-catlinks" class="mw-hidden-catlinks mw-hidden-cats-hidden">Hidden categories: <ul><li><a href="/wiki/Category:Articles_with_short_description" title="Category:Articles with short description">Articles with short description</a></li><li><a href="/wiki/Category:Short_description_matches_Wikidata" title="Category:Short description matches Wikidata">Short description matches Wikidata</a></li><li><a href="/wiki/Category:Commons_category_link_is_on_Wikidata" title="Category:Commons category link is on Wikidata">Commons category link is on Wikidata</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"> This page was last edited on 16 September 2024, at 00:21<span class="anonymous-show"> (UTC)</span>.</li> <li id="footer-info-copyright">Text is available under the <a href="/wiki/Wikipedia:Text_of_the_Creative_Commons_Attribution-ShareAlike_4.0_International_License" title="Wikipedia:Text of the Creative Commons Attribution-ShareAlike 4.0 International License">Creative Commons Attribution-ShareAlike 4.0 License</a>; additional terms may apply. By using this site, you agree to the <a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Terms_of_Use" class="extiw" title="foundation:Special:MyLanguage/Policy:Terms of Use">Terms of Use</a> and <a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Privacy_policy" class="extiw" title="foundation:Special:MyLanguage/Policy:Privacy policy">Privacy Policy</a>. Wikipedia® is a registered trademark of the <a rel="nofollow" class="external text" href="https://wikimediafoundation.org/">Wikimedia Foundation, Inc.</a>, a non-profit organization.</li> </ul> <ul id="footer-places"> <li id="footer-places-privacy"><a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Privacy_policy">Privacy policy</a></li> <li id="footer-places-about"><a href="/wiki/Wikipedia:About">About Wikipedia</a></li> <li id="footer-places-disclaimers"><a href="/wiki/Wikipedia:General_disclaimer">Disclaimers</a></li> <li id="footer-places-contact"><a href="//en.wikipedia.org/wiki/Wikipedia:Contact_us">Contact Wikipedia</a></li> <li id="footer-places-wm-codeofconduct"><a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Universal_Code_of_Conduct">Code of Conduct</a></li> <li id="footer-places-developers"><a href="https://developer.wikimedia.org">Developers</a></li> <li id="footer-places-statslink"><a href="https://stats.wikimedia.org/#/en.wikipedia.org">Statistics</a></li> <li id="footer-places-cookiestatement"><a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Cookie_statement">Cookie statement</a></li> <li id="footer-places-mobileview"><a href="//en.m.wikipedia.org/w/index.php?title=Atomic,_molecular,_and_optical_physics&mobileaction=toggle_view_mobile" class="noprint stopMobileRedirectToggle">Mobile view</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" lang="en" 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"><picture><source media="(min-width: 500px)" srcset="/w/resources/assets/poweredby_mediawiki.svg" width="88" height="31"><img src="/w/resources/assets/mediawiki_compact.svg" alt="Powered by MediaWiki" width="25" height="25" loading="lazy"></picture></a></li> </ul> </footer> </div> </div> </div> <div class="vector-header-container vector-sticky-header-container"> <div id="vector-sticky-header" class="vector-sticky-header"> <div class="vector-sticky-header-start"> <div class="vector-sticky-header-icon-start vector-button-flush-left vector-button-flush-right" aria-hidden="true"> <button class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-sticky-header-search-toggle" tabindex="-1" data-event-name="ui.vector-sticky-search-form.icon"><span class="vector-icon mw-ui-icon-search mw-ui-icon-wikimedia-search"></span> <span>Search</span> </button> </div> <div role="search" class="vector-search-box-vue vector-search-box-show-thumbnail vector-search-box"> <div class="vector-typeahead-search-container"> <div class="cdx-typeahead-search cdx-typeahead-search--show-thumbnail"> <form action="/w/index.php" id="vector-sticky-search-form" class="cdx-search-input cdx-search-input--has-end-button"> <div 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="Search Wikipedia"> <span class="cdx-text-input__icon cdx-text-input__start-icon"></span> </div> <input type="hidden" name="title" value="Special:Search"> </div> <button class="cdx-button cdx-search-input__end-button">Search</button> </form> </div> </div> </div> <div class="vector-sticky-header-context-bar"> <nav aria-label="Contents" class="vector-toc-landmark"> <div id="vector-sticky-header-toc" class="vector-dropdown mw-portlet mw-portlet-sticky-header-toc vector-sticky-header-toc vector-button-flush-left" > <input type="checkbox" id="vector-sticky-header-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-sticky-header-toc" class="vector-dropdown-checkbox " aria-label="Toggle the table of contents" > <label id="vector-sticky-header-toc-label" for="vector-sticky-header-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" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Toggle the table of contents</span> </label> <div class="vector-dropdown-content"> <div id="vector-sticky-header-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <div class="vector-sticky-header-context-bar-primary" aria-hidden="true" ><span class="mw-page-title-main">Atomic, molecular, and optical physics</span></div> </div> </div> <div class="vector-sticky-header-end" aria-hidden="true"> <div class="vector-sticky-header-icons"> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only" id="ca-talk-sticky-header" tabindex="-1" data-event-name="talk-sticky-header"><span class="vector-icon mw-ui-icon-speechBubbles mw-ui-icon-wikimedia-speechBubbles"></span> <span></span> </a> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only" id="ca-subject-sticky-header" tabindex="-1" data-event-name="subject-sticky-header"><span class="vector-icon mw-ui-icon-article mw-ui-icon-wikimedia-article"></span> <span></span> </a> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only" id="ca-history-sticky-header" tabindex="-1" data-event-name="history-sticky-header"><span class="vector-icon mw-ui-icon-wikimedia-history mw-ui-icon-wikimedia-wikimedia-history"></span> <span></span> </a> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only mw-watchlink" id="ca-watchstar-sticky-header" tabindex="-1" data-event-name="watch-sticky-header"><span class="vector-icon mw-ui-icon-wikimedia-star mw-ui-icon-wikimedia-wikimedia-star"></span> <span></span> </a> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only" id="ca-edit-sticky-header" tabindex="-1" data-event-name="wikitext-edit-sticky-header"><span class="vector-icon mw-ui-icon-wikimedia-wikiText mw-ui-icon-wikimedia-wikimedia-wikiText"></span> <span></span> </a> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only" id="ca-ve-edit-sticky-header" tabindex="-1" data-event-name="ve-edit-sticky-header"><span class="vector-icon mw-ui-icon-wikimedia-edit mw-ui-icon-wikimedia-wikimedia-edit"></span> <span></span> </a> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only" id="ca-viewsource-sticky-header" tabindex="-1" data-event-name="ve-edit-protected-sticky-header"><span class="vector-icon mw-ui-icon-wikimedia-editLock mw-ui-icon-wikimedia-wikimedia-editLock"></span> <span></span> </a> </div> <div class="vector-sticky-header-buttons"> <button class="cdx-button cdx-button--weight-quiet mw-interlanguage-selector" id="p-lang-btn-sticky-header" tabindex="-1" data-event-name="ui.dropdown-p-lang-btn-sticky-header"><span class="vector-icon mw-ui-icon-wikimedia-language mw-ui-icon-wikimedia-wikimedia-language"></span> <span>24 languages</span> </button> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive" id="ca-addsection-sticky-header" tabindex="-1" data-event-name="addsection-sticky-header"><span class="vector-icon mw-ui-icon-speechBubbleAdd-progressive mw-ui-icon-wikimedia-speechBubbleAdd-progressive"></span> <span>Add topic</span> </a> </div> <div class="vector-sticky-header-icon-end"> <div class="vector-user-links"> </div> </div> </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-b766959bd-lllpf","wgBackendResponseTime":117,"wgPageParseReport":{"limitreport":{"cputime":"0.767","walltime":"0.961","ppvisitednodes":{"value":6973,"limit":1000000},"postexpandincludesize":{"value":110102,"limit":2097152},"templateargumentsize":{"value":3184,"limit":2097152},"expansiondepth":{"value":16,"limit":100},"expensivefunctioncount":{"value":7,"limit":500},"unstrip-depth":{"value":1,"limit":20},"unstrip-size":{"value":169782,"limit":5000000},"entityaccesscount":{"value":1,"limit":400},"timingprofile":["100.00% 762.843 1 -total"," 30.48% 232.535 32 Template:Cite_book"," 23.06% 175.886 1 Template:Reflist"," 15.01% 114.510 16 Template:Rp"," 13.92% 106.222 16 Template:R/superscript"," 13.33% 101.721 1 Template:Quantum_mechanics"," 12.93% 98.619 1 Template:Sidebar_with_collapsible_lists"," 8.11% 61.876 1 Template:Short_description"," 7.18% 54.801 48 Template:R/where"," 6.08% 46.346 1 Template:Commons_category"]},"scribunto":{"limitreport-timeusage":{"value":"0.409","limit":"10.000"},"limitreport-memusage":{"value":6657657,"limit":52428800}},"cachereport":{"origin":"mw-web.codfw.main-5558bc8b6-sfm9h","timestamp":"20250210174159","ttl":2592000,"transientcontent":false}}});});</script> <script type="application/ld+json">{"@context":"https:\/\/schema.org","@type":"Article","name":"Atomic, molecular, and optical physics","url":"https:\/\/en.wikipedia.org\/wiki\/Atomic,_molecular,_and_optical_physics","sameAs":"http:\/\/www.wikidata.org\/entity\/Q1151533","mainEntity":"http:\/\/www.wikidata.org\/entity\/Q1151533","author":{"@type":"Organization","name":"Contributors to Wikimedia projects"},"publisher":{"@type":"Organization","name":"Wikimedia Foundation, Inc.","logo":{"@type":"ImageObject","url":"https:\/\/www.wikimedia.org\/static\/images\/wmf-hor-googpub.png"}},"datePublished":"2002-04-10T13:33:36Z","dateModified":"2024-09-16T00:21:46Z","headline":"study of matter-light interactions at small scales"}</script> </body> </html>