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[o]" accesskey="o" class=""><span>로그인</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="더 많은 옵션" > <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="개인 도구" > <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">개인 도구</span> </label> <div class="vector-dropdown-content"> <div id="p-personal" class="vector-menu mw-portlet mw-portlet-personal user-links-collapsible-item" title="사용자 메뉴" > <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="//donate.wikimedia.org/wiki/Special:FundraiserRedirector?utm_source=donate&utm_medium=sidebar&utm_campaign=C13_ko.wikipedia.org&uselang=ko"><span>기부</span></a></li><li id="pt-createaccount" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=%ED%8A%B9%EC%88%98:%EA%B3%84%EC%A0%95%EB%A7%8C%EB%93%A4%EA%B8%B0&returnto=%EC%8A%88%EB%A2%B0%EB%94%A9%EA%B1%B0+%EB%B0%A9%EC%A0%95%EC%8B%9D" title="계정을 만들고 로그인하는 것이 좋습니다. 하지만 필수는 아닙니다"><span class="vector-icon mw-ui-icon-userAdd mw-ui-icon-wikimedia-userAdd"></span> <span>계정 만들기</span></a></li><li id="pt-login" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=%ED%8A%B9%EC%88%98:%EB%A1%9C%EA%B7%B8%EC%9D%B8&returnto=%EC%8A%88%EB%A2%B0%EB%94%A9%EA%B1%B0+%EB%B0%A9%EC%A0%95%EC%8B%9D" title="위키백과에 로그인하면 여러가지 편리한 기능을 사용할 수 있습니다. [o]" accesskey="o"><span class="vector-icon mw-ui-icon-logIn mw-ui-icon-wikimedia-logIn"></span> <span>로그인</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"> 로그아웃한 편집자를 위한 문서 <a href="/wiki/%EB%8F%84%EC%9B%80%EB%A7%90:%EC%86%8C%EA%B0%9C" aria-label="편집에 관해 더 알아보기"><span>더 알아보기</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/%ED%8A%B9%EC%88%98:%EB%82%B4%EA%B8%B0%EC%97%AC" title="이 IP 주소의 편집 목록 [y]" accesskey="y"><span>기여</span></a></li><li id="pt-anontalk" class="mw-list-item"><a href="/wiki/%ED%8A%B9%EC%88%98:%EB%82%B4%EC%82%AC%EC%9A%A9%EC%9E%90%ED%86%A0%EB%A1%A0" title="현재 사용하는 IP 주소에 대한 토론 문서 [n]" accesskey="n"><span>토론</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="사이트"> <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="목차" 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">목차</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">사이드바로 이동</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">숨기기</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">처음 위치</div> </a> </li> <li id="toc-정의" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#정의"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>정의</span> </div> </a> <ul id="toc-정의-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-라그랑지언과_이차_양자화" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#라그랑지언과_이차_양자화"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>라그랑지언과 이차 양자화</span> </div> </a> <ul id="toc-라그랑지언과_이차_양자화-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-역사" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#역사"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>역사</span> </div> </a> <ul id="toc-역사-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-관련_방정식" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#관련_방정식"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>관련 방정식</span> </div> </a> <ul id="toc-관련_방정식-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-같이_보기" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#같이_보기"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>같이 보기</span> </div> </a> <ul id="toc-같이_보기-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-각주" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#각주"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>각주</span> </div> </a> <ul id="toc-각주-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-외부_링크" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#외부_링크"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>외부 링크</span> </div> </a> <ul id="toc-외부_링크-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="목차" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="목차 토글" > <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">목차 토글</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">슈뢰딩거 방정식</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="다른 언어로 문서를 방문합니다. 72개 언어로 읽을 수 있습니다" > <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-72" 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">72개 언어</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-af mw-list-item"><a href="https://af.wikipedia.org/wiki/Schr%C3%B6dinger-vergelyking" title="Schrödinger-vergelyking – 아프리칸스어" lang="af" hreflang="af" data-title="Schrödinger-vergelyking" data-language-autonym="Afrikaans" data-language-local-name="아프리칸스어" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%85%D8%B9%D8%A7%D8%AF%D9%84%D8%A9_%D8%B4%D8%B1%D9%88%D8%AF%D9%86%D8%BA%D8%B1" title="معادلة شرودنغر – 아랍어" lang="ar" hreflang="ar" data-title="معادلة شرودنغر" data-language-autonym="العربية" data-language-local-name="아랍어" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-arz mw-list-item"><a href="https://arz.wikipedia.org/wiki/%D9%85%D8%B9%D8%A7%D8%AF%D9%84%D8%A9_%D8%B4%D8%B1%D9%88%D8%AF%D9%8A%D9%86%D8%AC%D8%B1" title="معادلة شرودينجر – 이집트 아랍어" lang="arz" hreflang="arz" data-title="معادلة شرودينجر" data-language-autonym="مصرى" data-language-local-name="이집트 아랍어" class="interlanguage-link-target"><span>مصرى</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Ecuaci%C3%B3n_de_Schr%C3%B6dinger" title="Ecuación de Schrödinger – 아스투리아어" lang="ast" hreflang="ast" data-title="Ecuación de Schrödinger" data-language-autonym="Asturianu" data-language-local-name="아스투리아어" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/%C5%9Eredinger_t%C9%99nliyi" title="Şredinger tənliyi – 아제르바이잔어" lang="az" hreflang="az" data-title="Şredinger tənliyi" data-language-autonym="Azərbaycanca" data-language-local-name="아제르바이잔어" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%A3%D1%80%D0%B0%D1%9E%D0%BD%D0%B5%D0%BD%D0%BD%D0%B5_%D0%A8%D1%80%D0%BE%D0%B4%D0%B7%D1%96%D0%BD%D0%B3%D0%B5%D1%80%D0%B0" title="Ураўненне Шродзінгера – 벨라루스어" lang="be" hreflang="be" data-title="Ураўненне Шродзінгера" data-language-autonym="Беларуская" data-language-local-name="벨라루스어" 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%A3%D1%80%D0%B0%D0%B2%D0%BD%D0%B5%D0%BD%D0%B8%D0%B5_%D0%BD%D0%B0_%D0%A8%D1%80%D1%8C%D0%BE%D0%B4%D0%B8%D0%BD%D0%B3%D0%B5%D1%80" title="Уравнение на Шрьодингер – 불가리아어" lang="bg" hreflang="bg" data-title="Уравнение на Шрьодингер" data-language-autonym="Български" data-language-local-name="불가리아어" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%B6%E0%A7%8D%E0%A6%B0%E0%A7%8B%E0%A6%A1%E0%A6%BF%E0%A6%99%E0%A6%BE%E0%A6%B0_%E0%A6%B8%E0%A6%AE%E0%A7%80%E0%A6%95%E0%A6%B0%E0%A6%A3" title="শ্রোডিঙার সমীকরণ – 벵골어" lang="bn" hreflang="bn" data-title="শ্রোডিঙার সমীকরণ" data-language-autonym="বাংলা" data-language-local-name="벵골어" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Schr%C3%B6dingerova_jedna%C4%8Dina" title="Schrödingerova jednačina – 보스니아어" lang="bs" hreflang="bs" data-title="Schrödingerova jednačina" data-language-autonym="Bosanski" data-language-local-name="보스니아어" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Equaci%C3%B3_de_Schr%C3%B6dinger" title="Equació de Schrödinger – 카탈로니아어" lang="ca" hreflang="ca" data-title="Equació de Schrödinger" data-language-autonym="Català" data-language-local-name="카탈로니아어" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Schr%C3%B6dingerova_rovnice" title="Schrödingerova rovnice – 체코어" lang="cs" hreflang="cs" data-title="Schrödingerova rovnice" data-language-autonym="Čeština" data-language-local-name="체코어" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%A8%D1%80%D1%91%D0%B4%D0%B8%D0%BD%D0%B3%D0%B5%D1%80_%D1%82%D0%B0%D0%BD%D0%BB%C4%83%D1%85%C4%95" title="Шрёдингер танлăхĕ – 추바시어" lang="cv" hreflang="cv" data-title="Шрёдингер танлăхĕ" data-language-autonym="Чӑвашла" data-language-local-name="추바시어" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Schr%C3%B6dingers_ligning" title="Schrödingers ligning – 덴마크어" lang="da" hreflang="da" data-title="Schrödingers ligning" data-language-autonym="Dansk" data-language-local-name="덴마크어" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Schr%C3%B6dingergleichung" title="Schrödingergleichung – 독일어" lang="de" hreflang="de" data-title="Schrödingergleichung" data-language-autonym="Deutsch" data-language-local-name="독일어" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%95%CE%BE%CE%AF%CF%83%CF%89%CF%83%CE%B7_%CE%A3%CF%81%CE%AD%CE%BD%CF%84%CE%B9%CE%BD%CE%B3%CE%BA%CE%B5%CF%81" title="Εξίσωση Σρέντινγκερ – 그리스어" lang="el" hreflang="el" data-title="Εξίσωση Σρέντινγκερ" data-language-autonym="Ελληνικά" data-language-local-name="그리스어" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Schr%C3%B6dinger_equation" title="Schrödinger equation – 영어" lang="en" hreflang="en" data-title="Schrödinger equation" data-language-autonym="English" data-language-local-name="영어" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Ekvacio_de_Schr%C3%B6dinger" title="Ekvacio de Schrödinger – 에스페란토어" lang="eo" hreflang="eo" data-title="Ekvacio de Schrödinger" data-language-autonym="Esperanto" data-language-local-name="에스페란토어" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Ecuaci%C3%B3n_de_Schr%C3%B6dinger" title="Ecuación de Schrödinger – 스페인어" lang="es" hreflang="es" data-title="Ecuación de Schrödinger" data-language-autonym="Español" data-language-local-name="스페인어" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Schr%C3%B6dingeri_v%C3%B5rrand" title="Schrödingeri võrrand – 에스토니아어" lang="et" hreflang="et" data-title="Schrödingeri võrrand" data-language-autonym="Eesti" data-language-local-name="에스토니아어" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Schr%C3%B6dingerren_ekuazioa" title="Schrödingerren ekuazioa – 바스크어" lang="eu" hreflang="eu" data-title="Schrödingerren ekuazioa" data-language-autonym="Euskara" data-language-local-name="바스크어" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D9%85%D8%B9%D8%A7%D8%AF%D9%84%D9%87_%D8%B4%D8%B1%D9%88%D8%AF%DB%8C%D9%86%DA%AF%D8%B1" title="معادله شرودینگر – 페르시아어" lang="fa" hreflang="fa" data-title="معادله شرودینگر" data-language-autonym="فارسی" data-language-local-name="페르시아어" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Schr%C3%B6dingerin_yht%C3%A4l%C3%B6" title="Schrödingerin yhtälö – 핀란드어" lang="fi" hreflang="fi" data-title="Schrödingerin yhtälö" data-language-autonym="Suomi" data-language-local-name="핀란드어" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/%C3%89quation_de_Schr%C3%B6dinger" title="Équation de Schrödinger – 프랑스어" lang="fr" hreflang="fr" data-title="Équation de Schrödinger" data-language-autonym="Français" data-language-local-name="프랑스어" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Ecuaci%C3%B3n_de_Schr%C3%B6dinger" title="Ecuación de Schrödinger – 갈리시아어" lang="gl" hreflang="gl" data-title="Ecuación de Schrödinger" data-language-autonym="Galego" data-language-local-name="갈리시아어" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%9E%D7%A9%D7%95%D7%95%D7%90%D7%AA_%D7%A9%D7%A8%D7%93%D7%99%D7%A0%D7%92%D7%A8" title="משוואת שרדינגר – 히브리어" lang="he" hreflang="he" data-title="משוואת שרדינגר" data-language-autonym="עברית" data-language-local-name="히브리어" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%B6%E0%A5%8D%E0%A4%B0%E0%A5%8B%E0%A4%A1%E0%A4%BF%E0%A4%82%E0%A4%97%E0%A4%B0_%E0%A4%B8%E0%A4%AE%E0%A5%80%E0%A4%95%E0%A4%B0%E0%A4%A3" title="श्रोडिंगर समीकरण – 힌디어" lang="hi" hreflang="hi" data-title="श्रोडिंगर समीकरण" data-language-autonym="हिन्दी" data-language-local-name="힌디어" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Schr%C3%B6dingerova_jednad%C5%BEba" title="Schrödingerova jednadžba – 크로아티아어" lang="hr" hreflang="hr" data-title="Schrödingerova jednadžba" data-language-autonym="Hrvatski" data-language-local-name="크로아티아어" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Schr%C3%B6dinger-egyenlet" title="Schrödinger-egyenlet – 헝가리어" lang="hu" hreflang="hu" data-title="Schrödinger-egyenlet" data-language-autonym="Magyar" data-language-local-name="헝가리어" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D5%87%D6%80%D5%B5%D5%B8%D5%A4%D5%AB%D5%B6%D5%A3%D5%A5%D6%80%D5%AB_%D5%B0%D5%A1%D5%BE%D5%A1%D5%BD%D5%A1%D6%80%D5%B8%D6%82%D5%B4" title="Շրյոդինգերի հավասարում – 아르메니아어" lang="hy" hreflang="hy" data-title="Շրյոդինգերի հավասարում" data-language-autonym="Հայերեն" data-language-local-name="아르메니아어" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-ia mw-list-item"><a href="https://ia.wikipedia.org/wiki/Equation_de_Schr%C3%B6dinger" title="Equation de Schrödinger – 인터링구아" lang="ia" hreflang="ia" data-title="Equation de Schrödinger" data-language-autonym="Interlingua" data-language-local-name="인터링구아" class="interlanguage-link-target"><span>Interlingua</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Persamaan_Schr%C3%B6dinger" title="Persamaan Schrödinger – 인도네시아어" lang="id" hreflang="id" data-title="Persamaan Schrödinger" data-language-autonym="Bahasa Indonesia" data-language-local-name="인도네시아어" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/Jafna_Schr%C3%B6dingers" title="Jafna Schrödingers – 아이슬란드어" lang="is" hreflang="is" data-title="Jafna Schrödingers" data-language-autonym="Íslenska" data-language-local-name="아이슬란드어" class="interlanguage-link-target"><span>Íslenska</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Equazione_di_Schr%C3%B6dinger" title="Equazione di Schrödinger – 이탈리아어" lang="it" hreflang="it" data-title="Equazione di Schrödinger" data-language-autonym="Italiano" data-language-local-name="이탈리아어" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E3%82%B7%E3%83%A5%E3%83%AC%E3%83%BC%E3%83%87%E3%82%A3%E3%83%B3%E3%82%AC%E3%83%BC%E6%96%B9%E7%A8%8B%E5%BC%8F" title="シュレーディンガー方程式 – 일본어" lang="ja" hreflang="ja" data-title="シュレーディンガー方程式" data-language-autonym="日本語" data-language-local-name="일본어" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%A8%E1%83%A0%E1%83%94%E1%83%93%E1%83%98%E1%83%9C%E1%83%92%E1%83%94%E1%83%A0%E1%83%98%E1%83%A1_%E1%83%92%E1%83%90%E1%83%9C%E1%83%A2%E1%83%9D%E1%83%9A%E1%83%94%E1%83%91%E1%83%90" title="შრედინგერის განტოლება – 조지아어" lang="ka" hreflang="ka" data-title="შრედინგერის განტოლება" data-language-autonym="ქართული" data-language-local-name="조지아어" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-li mw-list-item"><a href="https://li.wikipedia.org/wiki/Schr%C3%B6dingervergelieking" title="Schrödingervergelieking – 림버거어" lang="li" hreflang="li" data-title="Schrödingervergelieking" data-language-autonym="Limburgs" data-language-local-name="림버거어" class="interlanguage-link-target"><span>Limburgs</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/%C5%A0r%C4%97dingerio_lygtis" title="Šrėdingerio lygtis – 리투아니아어" lang="lt" hreflang="lt" data-title="Šrėdingerio lygtis" data-language-autonym="Lietuvių" data-language-local-name="리투아니아어" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/%C5%A0r%C4%93dingera_vien%C4%81dojums" title="Šrēdingera vienādojums – 라트비아어" lang="lv" hreflang="lv" data-title="Šrēdingera vienādojums" data-language-autonym="Latviešu" data-language-local-name="라트비아어" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-mk badge-Q17437796 badge-featuredarticle mw-list-item" title="알찬 글"><a href="https://mk.wikipedia.org/wiki/%D0%A8%D1%80%D0%B5%D0%B4%D0%B8%D0%BD%D0%B3%D0%B5%D1%80%D0%BE%D0%B2%D0%B0_%D1%80%D0%B0%D0%B2%D0%B5%D0%BD%D0%BA%D0%B0" title="Шредингерова равенка – 마케도니아어" lang="mk" hreflang="mk" data-title="Шредингерова равенка" data-language-autonym="Македонски" data-language-local-name="마케도니아어" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-mn mw-list-item"><a href="https://mn.wikipedia.org/wiki/%D0%A8%D1%80%D0%B5%D0%B4%D0%B8%D0%BD%D0%B3%D0%B5%D1%80%D0%B8%D0%B9%D0%BD_%D1%82%D1%8D%D0%B3%D1%88%D0%B8%D1%82%D0%B3%D1%8D%D0%BB" title="Шредингерийн тэгшитгэл – 몽골어" lang="mn" hreflang="mn" data-title="Шредингерийн тэгшитгэл" data-language-autonym="Монгол" data-language-local-name="몽골어" class="interlanguage-link-target"><span>Монгол</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Persamaan_Schr%C3%B6dinger" title="Persamaan Schrödinger – 말레이어" lang="ms" hreflang="ms" data-title="Persamaan Schrödinger" data-language-autonym="Bahasa Melayu" data-language-local-name="말레이어" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-mt mw-list-item"><a href="https://mt.wikipedia.org/wiki/Ekwazzjoni_ta%27_Schr%C3%B6dinger" title="Ekwazzjoni ta' Schrödinger – 몰타어" lang="mt" hreflang="mt" data-title="Ekwazzjoni ta' Schrödinger" data-language-autonym="Malti" data-language-local-name="몰타어" class="interlanguage-link-target"><span>Malti</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Schr%C3%B6dingervergelijking" title="Schrödingervergelijking – 네덜란드어" lang="nl" hreflang="nl" data-title="Schrödingervergelijking" data-language-autonym="Nederlands" data-language-local-name="네덜란드어" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Schr%C3%B6dingerlikninga" title="Schrödingerlikninga – 노르웨이어(니노르스크)" lang="nn" hreflang="nn" data-title="Schrödingerlikninga" data-language-autonym="Norsk nynorsk" data-language-local-name="노르웨이어(니노르스크)" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Schr%C3%B6dinger-ligning" title="Schrödinger-ligning – 노르웨이어(보크말)" lang="nb" hreflang="nb" data-title="Schrödinger-ligning" data-language-autonym="Norsk bokmål" data-language-local-name="노르웨이어(보크말)" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-oc mw-list-item"><a href="https://oc.wikipedia.org/wiki/Equacion_de_Schr%C3%B6dinger" title="Equacion de Schrödinger – 오크어" lang="oc" hreflang="oc" data-title="Equacion de Schrödinger" data-language-autonym="Occitan" data-language-local-name="오크어" class="interlanguage-link-target"><span>Occitan</span></a></li><li class="interlanguage-link interwiki-pa mw-list-item"><a href="https://pa.wikipedia.org/wiki/%E0%A8%B8%E0%A8%BC%E0%A9%8D%E0%A8%B0%E0%A9%8B%E0%A8%A1%E0%A8%BF%E0%A9%B0%E0%A8%9C%E0%A8%B0_%E0%A8%87%E0%A8%95%E0%A9%81%E0%A8%8F%E0%A8%B8%E0%A8%BC%E0%A8%A8" title="ਸ਼੍ਰੋਡਿੰਜਰ ਇਕੁਏਸ਼ਨ – 펀잡어" lang="pa" hreflang="pa" data-title="ਸ਼੍ਰੋਡਿੰਜਰ ਇਕੁਏਸ਼ਨ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="펀잡어" class="interlanguage-link-target"><span>ਪੰਜਾਬੀ</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/R%C3%B3wnanie_Schr%C3%B6dingera" title="Równanie Schrödingera – 폴란드어" lang="pl" hreflang="pl" data-title="Równanie Schrödingera" data-language-autonym="Polski" data-language-local-name="폴란드어" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pnb mw-list-item"><a href="https://pnb.wikipedia.org/wiki/%D8%B4%D8%B1%D9%88%DA%88%D9%86%DA%AF%D8%B1_%D9%85%D8%B3%D8%A7%D9%88%D8%A7%D8%AA" title="شروڈنگر مساوات – Western Punjabi" lang="pnb" hreflang="pnb" data-title="شروڈنگر مساوات" data-language-autonym="پنجابی" data-language-local-name="Western Punjabi" class="interlanguage-link-target"><span>پنجابی</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Equa%C3%A7%C3%A3o_de_Schr%C3%B6dinger" title="Equação de Schrödinger – 포르투갈어" lang="pt" hreflang="pt" data-title="Equação de Schrödinger" data-language-autonym="Português" data-language-local-name="포르투갈어" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Ecua%C8%9Bia_lui_Schr%C3%B6dinger" title="Ecuația lui Schrödinger – 루마니아어" lang="ro" hreflang="ro" data-title="Ecuația lui Schrödinger" data-language-autonym="Română" data-language-local-name="루마니아어" 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%A3%D1%80%D0%B0%D0%B2%D0%BD%D0%B5%D0%BD%D0%B8%D0%B5_%D0%A8%D1%80%D1%91%D0%B4%D0%B8%D0%BD%D0%B3%D0%B5%D1%80%D0%B0" title="Уравнение Шрёдингера – 러시아어" lang="ru" hreflang="ru" data-title="Уравнение Шрёдингера" data-language-autonym="Русский" data-language-local-name="러시아어" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Schr%C3%B6dingerova_jedna%C4%8Dina" title="Schrödingerova jednačina – 세르비아-크로아티아어" lang="sh" hreflang="sh" data-title="Schrödingerova jednačina" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="세르비아-크로아티아어" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Schr%C3%B6dinger_equation" title="Schrödinger equation – Simple English" lang="en-simple" hreflang="en-simple" data-title="Schrödinger equation" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Schr%C3%B6dingerova_rovnica" title="Schrödingerova rovnica – 슬로바키아어" lang="sk" hreflang="sk" data-title="Schrödingerova rovnica" data-language-autonym="Slovenčina" data-language-local-name="슬로바키아어" 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/Schr%C3%B6dingerjeva_ena%C4%8Dba" title="Schrödingerjeva enačba – 슬로베니아어" lang="sl" hreflang="sl" data-title="Schrödingerjeva enačba" data-language-autonym="Slovenščina" data-language-local-name="슬로베니아어" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Ekuacioni_i_Shrodingerit" title="Ekuacioni i Shrodingerit – 알바니아어" lang="sq" hreflang="sq" data-title="Ekuacioni i Shrodingerit" data-language-autonym="Shqip" data-language-local-name="알바니아어" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%C5%A0redingerova_jedna%C4%8Dina" title="Šredingerova jednačina – 세르비아어" lang="sr" hreflang="sr" data-title="Šredingerova jednačina" data-language-autonym="Српски / srpski" data-language-local-name="세르비아어" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Schr%C3%B6dingerekvationen" title="Schrödingerekvationen – 스웨덴어" lang="sv" hreflang="sv" data-title="Schrödingerekvationen" data-language-autonym="Svenska" data-language-local-name="스웨덴어" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%9A%E0%AF%81%E0%AE%B0%E0%AF%8B%E0%AE%9F%E0%AE%BF%E0%AE%99%E0%AF%8D%E0%AE%95%E0%AE%B0%E0%AF%8D_%E0%AE%9A%E0%AE%AE%E0%AE%A9%E0%AF%8D%E0%AE%AA%E0%AE%BE%E0%AE%9F%E0%AF%81" title="சுரோடிங்கர் சமன்பாடு – 타밀어" lang="ta" hreflang="ta" data-title="சுரோடிங்கர் சமன்பாடு" data-language-autonym="தமிழ்" data-language-local-name="타밀어" 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%AA%E0%B8%A1%E0%B8%81%E0%B8%B2%E0%B8%A3%E0%B8%8A%E0%B9%80%E0%B8%A3%E0%B8%AD%E0%B8%94%E0%B8%B4%E0%B8%87%E0%B9%80%E0%B8%87%E0%B8%AD%E0%B8%A3%E0%B9%8C" title="สมการชเรอดิงเงอร์ – 태국어" lang="th" hreflang="th" data-title="สมการชเรอดิงเงอร์" data-language-autonym="ไทย" data-language-local-name="태국어" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tl mw-list-item"><a href="https://tl.wikipedia.org/wiki/Ekwasyong_Schr%C3%B6dinger" title="Ekwasyong Schrödinger – 타갈로그어" lang="tl" hreflang="tl" data-title="Ekwasyong Schrödinger" data-language-autonym="Tagalog" data-language-local-name="타갈로그어" class="interlanguage-link-target"><span>Tagalog</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Schr%C3%B6dinger_denklemi" title="Schrödinger denklemi – 터키어" lang="tr" hreflang="tr" data-title="Schrödinger denklemi" data-language-autonym="Türkçe" data-language-local-name="터키어" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-tt mw-list-item"><a href="https://tt.wikipedia.org/wiki/%D0%A8%D1%80%D3%A9%D0%B4%D0%B8%D0%BD%D0%B3%D0%B5%D1%80_%D1%82%D0%B8%D0%B3%D0%B5%D0%B7%D0%BB%D3%99%D0%BC%D3%99%D1%81%D0%B5" title="Шрөдингер тигезләмәсе – 타타르어" lang="tt" hreflang="tt" data-title="Шрөдингер тигезләмәсе" data-language-autonym="Татарча / tatarça" data-language-local-name="타타르어" class="interlanguage-link-target"><span>Татарча / tatarça</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%A0%D1%96%D0%B2%D0%BD%D1%8F%D0%BD%D0%BD%D1%8F_%D0%A8%D1%80%D0%B5%D0%B4%D1%96%D0%BD%D0%B3%D0%B5%D1%80%D0%B0" title="Рівняння Шредінгера – 우크라이나어" lang="uk" hreflang="uk" data-title="Рівняння Шредінгера" data-language-autonym="Українська" data-language-local-name="우크라이나어" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Shredinger_tenglamasi" title="Shredinger tenglamasi – 우즈베크어" lang="uz" hreflang="uz" data-title="Shredinger tenglamasi" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="우즈베크어" class="interlanguage-link-target"><span>Oʻzbekcha / 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href="mw-data:TemplateStyles:r36480591"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r36480591"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r36480591"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r36480591"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r36480591"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r36480591"><table class="sidebar sidebar-collapse nomobile nowraplinks plainlist nowraplinks" style="width:19.0em;"><tbody><tr><td class="sidebar-pretitle">관련 기사 시리즈의 일부</td></tr><tr><th class="sidebar-title-with-pretitle"><a href="/wiki/%EC%96%91%EC%9E%90%EC%97%AD%ED%95%99" title="양자역학">양자역학</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 {\partial }{\partial t}}|\psi (t)\rangle ={\hat {H}}|\psi (t)\rangle }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>i</mi> <mi class="MJX-variant">ℏ</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi mathvariant="normal">∂</mi> <mrow> <mi mathvariant="normal">∂</mi> <mi>t</mi> </mrow> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>ψ</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo fence="false" stretchy="false">⟩</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>H</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>ψ</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo fence="false" stretchy="false">⟩</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle i\hbar {\frac {\partial }{\partial t}}|\psi (t)\rangle ={\hat {H}}|\psi (t)\rangle }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0de8741a7d26ae98689c7b3339e97dfafea9fd26" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:21.692ex; height:5.509ex;" alt="{\displaystyle i\hbar {\frac {\partial }{\partial t}}|\psi (t)\rangle ={\hat {H}}|\psi (t)\rangle }"></span><div class="sidebar-caption" style="font-size:90%;padding-top:0.4em;font-style:italic;"><a class="mw-selflink selflink">슈뢰딩거 방정식</a></div></td></tr><tr><td class="sidebar-above hlist nowrap" style="display:block;margin-bottom:0.4em;"> <ul><li><a href="/wiki/%EC%96%91%EC%9E%90%EC%97%AD%ED%95%99_%EA%B0%9C%EB%A1%A0" title="양자역학 개론">개론</a></li> <li><a href="/wiki/%EC%96%91%EC%9E%90%EC%97%AD%ED%95%99%EC%9D%98_%EC%88%98%ED%95%99%EC%A0%81_%EA%B3%B5%EC%8B%9D%ED%99%94" class="mw-redirect" title="양자역학의 수학적 공식화">수학적 공식화</a></li> <li><a href="/wiki/%EC%96%91%EC%9E%90%EC%97%AD%ED%95%99%EC%9D%98_%EC%97%AD%EC%82%AC" title="양자역학의 역사">역사</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;">배경</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/%EA%B3%A0%EC%A0%84%EC%97%AD%ED%95%99" title="고전역학">고전역학</a></li> <li><a href="/wiki/%EC%B4%88%EA%B8%B0_%EC%96%91%EC%9E%90%EB%A1%A0" title="초기 양자론">초기 양자론</a></li> <li><a href="/wiki/%EB%B8%8C%EB%9D%BC-%EC%BC%93_%ED%91%9C%EA%B8%B0%EB%B2%95" title="브라-켓 표기법">브라-켓 표기법</a></li></ul> <div class="hlist"> <ul><li><a href="/wiki/%ED%95%B4%EB%B0%80%ED%86%A0%EB%8B%88%EC%96%B8_(%EC%96%91%EC%9E%90%EC%97%AD%ED%95%99)" title="해밀토니언 (양자역학)">해밀토니언</a></li> <li><a href="/wiki/%EA%B0%84%EC%84%AD_(%ED%8C%8C%EB%8F%99_%EC%A0%84%ED%8C%8C)" title="간섭 (파동 전파)">간섭</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;">기본</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/%EC%83%81%EB%B3%B4%EC%84%B1_(%EB%AC%BC%EB%A6%AC%ED%95%99)" title="상보성 (물리학)">상보성</a></li> <li><a href="/wiki/%EC%96%91%EC%9E%90_%EA%B2%B0%EC%96%B4%EA%B8%8B%EB%82%A8" title="양자 결어긋남">결어긋남</a></li> <li><a href="/wiki/%EC%96%91%EC%9E%90_%EC%96%BD%ED%9E%98" title="양자 얽힘">얽힘</a></li> <li><a href="/wiki/%EC%97%90%EB%84%88%EC%A7%80_%EC%A4%80%EC%9C%84" title="에너지 준위">에너지 준위</a></li> <li><a href="https://en.wikipedia.org/wiki/Measurement_in_quantum_mechanics" class="extiw" title="w:Measurement in quantum mechanics">측정(measurement)</a></li> <li><a href="https://en.wikipedia.org/wiki/Quantum_nonlocality" class="extiw" title="w:Quantum nonlocality">비국소성(nonlocality)</a></li> <li><a href="/wiki/%EC%96%91%EC%9E%90%EC%88%98" title="양자수">양자수</a></li> <li><a href="https://en.wikipedia.org/wiki/Quantum_state" class="extiw" title="w:Quantum state">상태(state)</a></li> <li><a href="/wiki/%EC%96%91%EC%9E%90_%EC%A4%91%EC%B2%A9" title="양자 중첩">중첩</a></li> <li><a href="https://en.wikipedia.org/wiki/Symmetry_in_quantum_mechanics" class="extiw" title="w:Symmetry in quantum mechanics">Symmetry</a></li> <li><a href="/wiki/%ED%84%B0%EB%84%90_%ED%9A%A8%EA%B3%BC" title="터널 효과">터널링</a></li> <li><a href="/wiki/%EB%B6%88%ED%99%95%EC%A0%95%EC%84%B1_%EC%9B%90%EB%A6%AC" title="불확정성 원리">불확정성</a></li> <li><a href="/wiki/%ED%8C%8C%EB%8F%99_%ED%95%A8%EC%88%98" title="파동 함수">파동 함수</a> <ul><li><a href="/wiki/%ED%8C%8C%EB%8F%99_%ED%95%A8%EC%88%98_%EB%B6%95%EA%B4%B4" title="파동 함수 붕괴">붕괴</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;">실험</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/%EB%B2%A8_%EB%B6%80%EB%93%B1%EC%8B%9D_%EC%8B%A4%ED%97%98" title="벨 부등식 실험">벨 부등식</a></li> <li><a href="/wiki/%EB%8D%B0%EC%9D%B4%EB%B9%84%EC%8A%A8-%EA%B1%B0%EB%A8%B8_%EC%8B%A4%ED%97%98" title="데이비슨-거머 실험">데이비슨-거머</a></li> <li><a href="/wiki/%EC%9D%B4%EC%A4%91%EC%8A%AC%EB%A6%BF_%EC%8B%A4%ED%97%98" title="이중슬릿 실험">이중슬릿</a></li> <li><a href="https://en.wikipedia.org/wiki/Elitzur%E2%80%93Vaidman_bomb_tester" class="extiw" title="w:Elitzur–Vaidman bomb tester">엘리추르–바이드만(Elitzur–Vaidman)</a></li> <li><a href="/wiki/%ED%94%84%EB%9E%91%ED%81%AC-%ED%97%A4%EB%A5%B4%EC%B8%A0_%EC%8B%A4%ED%97%98" title="프랑크-헤르츠 실험">프랑크-헤르츠</a></li> <li><a href="https://en.wikipedia.org/wiki/Leggett%E2%80%93Garg_inequality" class="extiw" title="w:Leggett–Garg inequality">레게트-가르그 부등식(Leggett–Garg inequality)</a></li> <li><a href="https://en.wikipedia.org/wiki/Mach%E2%80%93Zehnder_interferometer" class="extiw" title="w:Mach–Zehnder interferometer">마하-젠더(Mach–Zehnder)</a></li> <li><a href="https://en.wikipedia.org/wiki/Popper%27s_experiment" class="extiw" title="w:Popper's experiment">포퍼(Popper)</a></li></ul> </div> <ul><li><a href="https://en.wikipedia.org/wiki/Quantum_eraser_experiment" class="extiw" title="w:Quantum eraser experiment">양자 지우개(quantum eraser)</a> <ul><li><a href="/wiki/%EC%A7%80%EC%97%B0%EC%84%A0%ED%83%9D_%EC%96%91%EC%9E%90_%EC%A7%80%EC%9A%B0%EA%B0%9C" title="지연선택 양자 지우개">지연선택</a></li></ul></li></ul> <div class="hlist"> <ul><li><a href="/wiki/%EC%8A%88%EB%A2%B0%EB%94%A9%EA%B1%B0%EC%9D%98_%EA%B3%A0%EC%96%91%EC%9D%B4" title="슈뢰딩거의 고양이">슈뢰딩거의 고양이</a></li> <li><a href="/wiki/%EC%8A%88%ED%85%8C%EB%A5%B8-%EA%B2%8C%EB%A5%BC%EB%9D%BC%ED%9D%90_%EC%8B%A4%ED%97%98" title="슈테른-게를라흐 실험">슈테른-게를라흐</a></li> <li><a href="https://en.wikipedia.org/wiki/Wheeler%27s_delayed-choice_experiment" class="extiw" title="w:Wheeler's delayed-choice experiment">휠러의 지연된 선택(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;">공식화</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/%EC%96%91%EC%9E%90%EC%97%AD%ED%95%99%EC%9D%98_%EC%88%98%ED%95%99_%EA%B3%B5%EC%8B%9D%ED%99%94" title="양자역학의 수학 공식화">개요</a></li></ul> <div class="hlist"> <ul><li><a href="/wiki/%ED%95%98%EC%9D%B4%EC%A0%A0%EB%B2%A0%EB%A5%B4%ED%81%AC_%EB%AC%98%EC%82%AC" title="하이젠베르크 묘사">하이젠베르크</a></li> <li><a href="/wiki/%EC%83%81%ED%98%B8%EC%9E%91%EC%9A%A9_%EB%AC%98%EC%82%AC" title="상호작용 묘사">상호작용 묘사</a></li> <li><a href="/wiki/%ED%96%89%EB%A0%AC_%EC%97%AD%ED%95%99" title="행렬 역학">행렬</a></li> <li><a href="https://en.wikipedia.org/wiki/Phase_space_formulation" class="extiw" title="w:Phase space formulation">Phase-space</a></li> <li><a href="/wiki/%EC%8A%88%EB%A2%B0%EB%94%A9%EA%B1%B0_%EB%AC%98%EC%82%AC" title="슈뢰딩거 묘사">슈뢰딩거</a></li> <li><a href="/wiki/%EA%B2%BD%EB%A1%9C_%EC%A0%81%EB%B6%84_%EA%B3%B5%EC%8B%9D%ED%99%94" title="경로 적분 공식화">합계 기록(경로 적분)</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;">방정식</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/%EB%94%94%EB%9E%99_%EB%B0%A9%EC%A0%95%EC%8B%9D" title="디랙 방정식">디랙</a></li> <li><a href="/wiki/%ED%81%B4%EB%9D%BC%EC%9D%B8-%EA%B3%A0%EB%93%A0_%EB%B0%A9%EC%A0%95%EC%8B%9D" title="클라인-고든 방정식">클라인-고든</a></li> <li><a href="https://en.wikipedia.org/wiki/Pauli_equation" class="extiw" title="w:Pauli equation">파울리(Pauli)</a></li> <li><a href="/wiki/%EB%A4%BC%EB%93%9C%EB%B2%A0%EB%A6%AC_%EA%B3%B5%EC%8B%9D" title="뤼드베리 공식">뤼드베리</a></li> <li><a class="mw-selflink selflink">슈뢰딩거</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;"><a href="/wiki/%EC%96%91%EC%9E%90%EC%97%AD%ED%95%99%EC%9D%98_%ED%95%B4%EC%84%9D" title="양자역학의 해석">해석</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/%EC%96%91%EC%9E%90_%EB%B2%A0%EC%9D%B4%EC%A6%88%EC%A3%BC%EC%9D%98" title="양자 베이즈주의">베이지안</a></li> <li><a href="/wiki/%EC%A0%95%ED%95%A9%EC%A0%81_%EC%97%AD%EC%82%AC" title="정합적 역사">정합적 역사</a></li> <li><a href="/wiki/%EC%BD%94%ED%8E%9C%ED%95%98%EA%B2%90_%ED%95%B4%EC%84%9D" title="코펜하겐 해석">코펜하겐</a></li> <li><a href="/wiki/%EB%93%9C_%EB%B8%8C%EB%A1%9C%EC%9D%B4-%EB%B4%84_%EC%9D%B4%EB%A1%A0" title="드 브로이-봄 이론">드 브로이-봄</a></li> <li><a href="/wiki/%EC%95%99%EC%83%81%EB%B8%94_%ED%95%B4%EC%84%9D" title="앙상블 해석">앙상블</a></li> <li><a href="/wiki/%EC%88%A8%EC%9D%80_%EB%B3%80%EC%88%98_%EC%9D%B4%EB%A1%A0" title="숨은 변수 이론">숨은 변수</a> <ul><li><a href="/wiki/%EA%B5%AD%EC%86%8C%EC%A0%81_%EC%88%A8%EC%9D%80_%EB%B3%80%EC%88%98_%EC%9D%B4%EB%A1%A0" title="국소적 숨은 변수 이론">국소적</a></li></ul></li> <li><a href="/wiki/%EB%8B%A4%EC%84%B8%EA%B3%84_%ED%95%B4%EC%84%9D" title="다세계 해석">다세계</a></li> <li><a href="/wiki/%EA%B0%9D%EA%B4%80%EC%A0%81_%EB%B6%95%EA%B4%B4_%EC%9D%B4%EB%A1%A0" title="객관적 붕괴 이론">객관적 붕괴</a></li> <li><a href="/wiki/%EC%96%91%EC%9E%90_%EB%85%BC%EB%A6%AC" title="양자 논리">양자 논리</a></li> <li><a href="/wiki/%EA%B4%80%EA%B3%84%EC%A0%81_%EC%96%91%EC%9E%90_%EC%97%AD%ED%95%99" title="관계적 양자 역학">관계적</a></li> <li><a href="https://en.wikipedia.org/wiki/Transactional_interpretation" class="extiw" title="w:Transactional interpretation">트랜잭션(transactional)</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;">고급 주제</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/%EC%83%81%EB%8C%80%EB%A1%A0%EC%A0%81_%EC%96%91%EC%9E%90%EC%97%AD%ED%95%99" title="상대론적 양자역학">상대론적 양자역학</a></li> <li><a href="/wiki/%EC%96%91%EC%9E%90%EC%9E%A5%EB%A1%A0" title="양자장론">양자장론</a></li> <li><a href="/wiki/%EC%96%91%EC%9E%90_%EC%A0%95%EB%B3%B4_%EA%B3%BC%ED%95%99" class="mw-redirect" title="양자 정보 과학">양자 정보 과학</a></li> <li><a href="https://en.wikipedia.org/wiki/Quantum_computing" class="extiw" title="w:Quantum computing">양자 컴퓨팅(quantum computing)</a></li> <li><a href="https://en.wikipedia.org/wiki/Quantum_chaos" class="extiw" title="w:Quantum chaos">양자 카오스(quantum chaos)</a></li> <li><a href="/wiki/EPR_%EC%97%AD%EC%84%A4" title="EPR 역설">EPR 역설</a></li> <li><a href="/wiki/%EB%B0%80%EB%8F%84_%ED%96%89%EB%A0%AC" title="밀도 행렬">밀도 행렬</a></li> <li><a href="/wiki/%EC%82%B0%EB%9E%80_%EC%9D%B4%EB%A1%A0" title="산란 이론">산란 이론</a></li> <li><a href="/wiki/%EC%96%91%EC%9E%90%ED%86%B5%EA%B3%84%EC%97%AD%ED%95%99" title="양자통계역학">양자통계역학</a></li> <li><a href="https://en.wikipedia.org/wiki/Quantum_machine_learning" class="extiw" title="w:Quantum machine learning">양자 기계 학습(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;">과학자</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="https://en.wikipedia.org/wiki/Yakir_Aharonov" class="extiw" title="w:Yakir Aharonov">아하로노프<sub>Aharonov</sub></a></li> <li><a href="/wiki/%EC%A1%B4_%EC%8A%A4%ED%8A%9C%EC%96%B4%ED%8A%B8_%EB%B2%A8" title="존 스튜어트 벨">벨</a></li> <li><a href="/wiki/%ED%95%9C%EC%8A%A4_%EB%B2%A0%ED%85%8C" title="한스 베테">베테</a></li> <li><a href="/wiki/%ED%8C%A8%ED%8A%B8%EB%A6%AD_%EB%B8%94%EB%9E%98%ED%82%B7" title="패트릭 블래킷">블래킷</a></li> <li><a href="/wiki/%ED%8E%A0%EB%A6%AD%EC%8A%A4_%EB%B8%94%EB%A1%9C%ED%9D%90" title="펠릭스 블로흐">블로흐</a></li> <li><a href="/wiki/%EB%8D%B0%EC%9D%B4%EB%B9%84%EB%93%9C_%EB%B4%84" title="데이비드 봄">봄</a></li> <li><a href="/wiki/%EB%8B%90%EC%8A%A4_%EB%B3%B4%EC%96%B4" title="닐스 보어">보어</a></li> <li><a href="/wiki/%EB%A7%89%EC%8A%A4_%EB%B3%B4%EB%A5%B8" title="막스 보른">보른</a></li> <li><a href="/wiki/%EC%82%AC%ED%8B%B0%EC%97%94%EB%93%9C%EB%9D%BC_%EB%82%98%ED%8A%B8_%EB%B3%B4%EC%8A%A4" title="사티엔드라 나트 보스">보스</a></li> <li><a href="/wiki/%EB%A3%A8%EC%9D%B4_%EB%93%9C_%EB%B8%8C%EB%A1%9C%EC%9D%B4" title="루이 드 브로이">드브로이</a></li> <li><a href="/wiki/%EC%95%84%EC%84%9C_%EC%BD%A4%ED%94%84%ED%84%B4" title="아서 콤프턴">콤프턴</a></li> <li><a href="/wiki/%ED%8F%B4_%EB%94%94%EB%9E%99" title="폴 디랙">디랙</a></li> <li><a href="/wiki/%ED%81%B4%EB%A6%B0%ED%84%B4_%EC%A1%B0%EC%A7%80%ED%94%84_%EB%8D%B0%EC%9D%B4%EB%B9%84%EC%8A%A8" title="클린턴 조지프 데이비슨">데이비슨</a></li> <li><a href="/wiki/%ED%94%BC%ED%84%B0_%EB%94%94%EB%B0%94%EC%9D%B4" title="피터 디바이">디바이</a></li> <li><a href="/wiki/%ED%8C%8C%EC%9A%B8_%EC%97%90%EB%A0%8C%ED%8E%98%EC%8A%A4%ED%8A%B8" title="파울 에렌페스트">에렌페스트</a></li> <li><a href="/wiki/%EC%95%8C%EB%B2%A0%EB%A5%B4%ED%8A%B8_%EC%95%84%EC%9D%B8%EC%8A%88%ED%83%80%EC%9D%B8" title="알베르트 아인슈타인">아인슈타인</a></li> <li><a href="/wiki/%ED%9C%B4_%EC%97%90%EB%B2%84%EB%A0%9B_3%EC%84%B8" title="휴 에버렛 3세">에버렛</a></li> <li><a href="/wiki/%EB%B8%94%EB%9D%BC%EB%94%94%EB%AF%B8%EB%A5%B4_%ED%8F%AC%ED%81%AC" title="블라디미르 포크">포크</a></li> <li><a href="/wiki/%EC%97%94%EB%A6%AC%EC%BD%94_%ED%8E%98%EB%A5%B4%EB%AF%B8" title="엔리코 페르미">페르미</a></li> <li><a href="/wiki/%EB%A6%AC%EC%B2%98%EB%93%9C_%ED%8C%8C%EC%9D%B8%EB%A8%BC" class="mw-redirect" title="리처드 파인먼">파인먼</a></li> <li><a href="/wiki/%EB%A1%9C%EC%9D%B4_J._%EA%B8%80%EB%9D%BC%EC%9A%B0%EB%B2%84" title="로이 J. 글라우버">글라우버</a></li> <li><a href="https://en.wikipedia.org/wiki/Martin_Gutzwiller" class="extiw" title="w:Martin Gutzwiller">구츠윌러<sub>Gutzwiller</sub></a></li> <li><a href="/wiki/%EB%B2%A0%EB%A5%B4%EB%84%88_%ED%95%98%EC%9D%B4%EC%A0%A0%EB%B2%A0%EB%A5%B4%ED%81%AC" title="베르너 하이젠베르크">하이젠베르크</a></li> <li><a href="/wiki/%EB%8B%A4%EB%B9%84%ED%8A%B8_%ED%9E%90%EB%B2%A0%EB%A5%B4%ED%8A%B8" title="다비트 힐베르트">힐베르트</a></li> <li><a href="/wiki/%ED%8C%8C%EC%8A%A4%EC%BF%A0%EC%95%8C_%EC%9A%94%EB%A5%B4%EB%8B%A8" title="파스쿠알 요르단">요르단</a></li> <li><a href="/wiki/%ED%97%A8%EB%93%9C%EB%A6%AD_%EC%95%88%ED%86%A0%EB%8B%88_%ED%81%AC%EB%9D%BC%EB%A8%B8%EB%A5%B4%EC%8A%A4" title="헨드릭 안토니 크라머르스">크라머르스</a></li> <li><a href="/wiki/%EB%B3%BC%ED%94%84%EA%B0%95_%ED%8C%8C%EC%9A%B8%EB%A6%AC" title="볼프강 파울리">파울리</a></li> <li><a href="/wiki/%EC%9C%8C%EB%A6%AC%EC%8A%A4_%EC%9C%A0%EC%A7%84_%EB%9E%A8" title="윌리스 유진 램">램</a></li> <li><a href="/wiki/%EB%A0%88%ED%94%84_%EB%9E%80%EB%8B%A4%EC%9A%B0" title="레프 란다우">란다우</a></li> <li><a href="/wiki/%EB%A7%89%EC%8A%A4_%ED%8F%B0_%EB%9D%BC%EC%9A%B0%EC%97%90" title="막스 폰 라우에">라우에</a></li> <li><a href="/wiki/%ED%97%A8%EB%A6%AC_%EB%AA%A8%EC%A6%90%EB%A6%AC_(%EB%AC%BC%EB%A6%AC%ED%95%99%EC%9E%90)" title="헨리 모즐리 (물리학자)">모즐리</a></li> <li><a href="/wiki/%EB%A1%9C%EB%B2%84%ED%8A%B8_%EC%95%A4%EB%93%9C%EB%A3%A8%EC%8A%A4_%EB%B0%80%EB%A6%AC%EC%BB%A8" title="로버트 앤드루스 밀리컨">밀리컨</a></li> <li><a href="/wiki/%ED%97%A4%EC%9D%B4%EC%BB%A4_%EC%B9%B4%EB%A9%94%EB%A5%BC%EB%A7%81_%EC%98%A4%EB%84%88%EC%8A%A4" title="헤이커 카메를링 오너스">오너스</a></li> <li><a href="/wiki/%EB%A7%89%EC%8A%A4_%ED%94%8C%EB%9E%91%ED%81%AC" title="막스 플랑크">플랑크</a></li> <li><a href="/wiki/%EC%9D%B4%EC%A7%80%EB%8F%84%EC%96%B4_%EC%95%84%EC%9D%B4%EC%9E%91_%EB%9D%BC%EB%B9%84" title="이지도어 아이작 라비">라비</a></li> <li><a href="/wiki/%EC%B0%AC%EB%93%9C%EB%9D%BC%EC%84%B8%EC%B9%B4%EB%9D%BC_%EB%B2%B5%EC%B9%B4%ED%83%80_%EB%9D%BC%EB%A7%8C" title="찬드라세카라 벵카타 라만">라만</a></li> <li><a href="/wiki/%EC%9A%94%ED%95%9C%EB%84%A4%EC%8A%A4_%EB%A4%BC%EB%93%9C%EB%B2%A0%EB%A6%AC" title="요한네스 뤼드베리">뤼드베리</a></li> <li><a href="/wiki/%EC%97%90%EB%A5%B4%EB%B9%88_%EC%8A%88%EB%A2%B0%EB%94%A9%EA%B1%B0" title="에르빈 슈뢰딩거">슈뢰딩거</a></li> <li><a href="https://en.wikipedia.org/wiki/Michelle_Simmons" class="extiw" title="w:Michelle Simmons">시몬스<sub>Simmons</sub></a></li> <li><a href="/wiki/%EC%95%84%EB%A5%B4%EB%86%80%ED%8A%B8_%EC%A1%B0%EB%A8%B8%ED%8E%A0%ED%8A%B8" title="아르놀트 조머펠트">조머펠트</a></li> <li><a href="/wiki/%EC%A1%B4_%ED%8F%B0_%EB%85%B8%EC%9D%B4%EB%A7%8C" title="존 폰 노이만">폰 노이만</a></li> <li><a href="/wiki/%ED%97%A4%EB%A5%B4%EB%A7%8C_%EB%B0%94%EC%9D%BC" title="헤르만 바일">바일</a></li> <li><a href="/wiki/%EB%B9%8C%ED%97%AC%EB%A6%84_%EB%B9%88" title="빌헬름 빈">빈</a></li> <li><a href="/wiki/%EC%9C%A0%EC%A7%84_%EC%9C%84%EA%B7%B8%EB%84%88" title="유진 위그너">위그너</a></li> <li><a href="/wiki/%ED%94%BC%ED%84%B0%EB%A5%B4_%EC%A0%9C%EC%9D%B4%EB%A7%8C" title="피터르 제이만">제이만</a></li> <li><a href="/wiki/%EC%95%88%ED%86%A4_%EC%B0%A8%EC%9D%BC%EB%A7%81%EA%B1%B0" title="안톤 차일링거">차일링거</a></li></ul> </div></div></div></td> </tr><tr><td class="sidebar-navbar" style="border-top:1px solid #aaa;padding-top:0.1em; [[분류:역학 틀]] [[분류:물리학 사이드바 틀]]"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r36480591"><style data-mw-deduplicate="TemplateStyles:r34311309">.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}</style><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-보기"><a href="/wiki/%ED%8B%80:%EC%96%91%EC%9E%90%EC%97%AD%ED%95%99" title="틀:양자역학"><abbr title="이 틀을 보기">v</abbr></a></li><li class="nv-토론"><a href="/wiki/%ED%8B%80%ED%86%A0%EB%A1%A0:%EC%96%91%EC%9E%90%EC%97%AD%ED%95%99" title="틀토론:양자역학"><abbr title="이 틀에 관해 토론하기">t</abbr></a></li><li class="nv-편집"><a href="/wiki/%ED%8A%B9%EC%88%98:%EB%AC%B8%EC%84%9C%ED%8E%B8%EC%A7%91/%ED%8B%80:%EC%96%91%EC%9E%90%EC%97%AD%ED%95%99" title="특수:문서편집/틀:양자역학"><abbr title="이 틀을 편집하기">e</abbr></a></li></ul></div></td></tr></tbody></table> <figure typeof="mw:File/Thumb"><a href="/wiki/%ED%8C%8C%EC%9D%BC:Erwin_Schr%C3%B6dinger_(1933).jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/2e/Erwin_Schr%C3%B6dinger_%281933%29.jpg/180px-Erwin_Schr%C3%B6dinger_%281933%29.jpg" decoding="async" width="180" height="255" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/2e/Erwin_Schr%C3%B6dinger_%281933%29.jpg/270px-Erwin_Schr%C3%B6dinger_%281933%29.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/2/2e/Erwin_Schr%C3%B6dinger_%281933%29.jpg 2x" data-file-width="280" data-file-height="396" /></a><figcaption><a href="/wiki/%EC%97%90%EB%A5%B4%EB%B9%88_%EC%8A%88%EB%A2%B0%EB%94%A9%EA%B1%B0" title="에르빈 슈뢰딩거">에르빈 슈뢰딩거</a></figcaption></figure> <p><b>슈뢰딩거 방정식</b>(-方程式, <span style="font-size: smaller;"><a href="/wiki/%EC%98%81%EC%96%B4" title="영어">영어</a>: </span><span lang="en">Schrödinger equation</span>)은 비<a href="/wiki/%EC%83%81%EB%8C%80%EB%A1%A0" class="mw-redirect" title="상대론">상대론</a>적 <a href="/wiki/%EC%96%91%EC%9E%90%EC%97%AD%ED%95%99" title="양자역학">양자역학</a>적 계의 시간에 따른 진화를 나타내는 선형 <a href="/wiki/%ED%8E%B8%EB%AF%B8%EB%B6%84_%EB%B0%A9%EC%A0%95%EC%8B%9D" title="편미분 방정식">편미분 방정식</a>이다. <a href="/wiki/%EC%98%A4%EC%8A%A4%ED%8A%B8%EB%A6%AC%EC%95%84" title="오스트리아">오스트리아</a>의 <a href="/wiki/%EB%AC%BC%EB%A6%AC%ED%95%99%EC%9E%90" title="물리학자">물리학자</a> <a href="/wiki/%EC%97%90%EB%A5%B4%EB%B9%88_%EC%8A%88%EB%A2%B0%EB%94%A9%EA%B1%B0" title="에르빈 슈뢰딩거">에르빈 슈뢰딩거</a>가 도입하였고,<sup id="cite_ref-Schrödinger25_1-0" class="reference"><a href="#cite_note-Schrödinger25-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> 그가 발명한 <a href="/wiki/%ED%8C%8C%EB%8F%99%EC%97%AD%ED%95%99" title="파동역학">파동역학</a>의 기본 <a href="/wiki/%EB%B0%A9%EC%A0%95%EC%8B%9D" title="방정식">방정식</a>이다. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="정의"><span id=".EC.A0.95.EC.9D.98"></span>정의</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%EC%8A%88%EB%A2%B0%EB%94%A9%EA%B1%B0_%EB%B0%A9%EC%A0%95%EC%8B%9D&action=edit&section=1" title="부분 편집: 정의"><span>편집</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/%ED%8C%8C%EB%8F%99_%ED%95%A8%EC%88%98" title="파동 함수">파동 함수</a> <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 \psi (x)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ψ</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \psi (x)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a596a1fb4130a47f6b88c66150497338bd6cbccc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.652ex; height:2.843ex;" alt="{\displaystyle \psi (x)}"></span>에 대한 슈뢰딩거 방정식은 다음과 같다. </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 i\hbar {\frac {\partial {}|\psi \rangle }{\partial {}t}}={\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> <mrow> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>ψ</mi> <mo fence="false" stretchy="false">⟩</mo> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> </mrow> <mi>t</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>H</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>ψ</mi> <mo fence="false" stretchy="false">⟩</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle i\hbar {\frac {\partial {}|\psi \rangle }{\partial {}t}}={\hat {H}}|\psi \rangle }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/83371b310b9a7700694a5c6e8d5cb2d228cfb08e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:15.555ex; height:5.843ex;" alt="{\displaystyle i\hbar {\frac {\partial {}|\psi \rangle }{\partial {}t}}={\hat {H}}|\psi \rangle }"></span></dd></dl> <p><a href="/wiki/%ED%95%B4%EB%B0%80%ED%86%A0%EB%8B%88%EC%96%B8_(%EC%96%91%EC%9E%90%EC%97%AD%ED%95%99)" title="해밀토니언 (양자역학)">해밀토니언</a> <a href="/wiki/%EC%97%B0%EC%82%B0%EC%9E%90" title="연산자">연산자</a> <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 {\hat {H}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>H</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\hat {H}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6bb06de5217295d7fbdbf68fb9c5309a513fc99e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.064ex; height:2.843ex;" alt="{\displaystyle {\hat {H}}}"></span>는 고전적 <a href="/wiki/%ED%95%B4%EB%B0%80%ED%86%A0%EB%8B%88%EC%96%B8" class="mw-disambig" title="해밀토니언">해밀토니언</a>에 해당하는 연산자로, 후자를 <a href="/wiki/%EC%96%91%EC%9E%90%ED%99%94_(%EB%AC%BC%EB%A6%AC%ED%95%99)" title="양자화 (물리학)">양자화</a>하여 얻는다. <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 |\psi \rangle }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>ψ</mi> <mo fence="false" stretchy="false">⟩</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle |\psi \rangle }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cc27f1893b769a08cd6b296e115a29e61cab675e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:3.065ex; height:2.843ex;" alt="{\displaystyle |\psi \rangle }"></span>는 <a href="/wiki/%ED%8F%B4_%EB%94%94%EB%9E%99" title="폴 디랙">폴 디랙</a>의 <a href="/wiki/%EB%B8%8C%EB%9D%BC-%EC%BC%93_%ED%91%9C%EA%B8%B0" class="mw-redirect" title="브라-켓 표기">브라-켓 표기</a>를 사용해 나타낸, <a href="/wiki/%EC%8A%88%EB%A2%B0%EB%94%A9%EA%B1%B0_%EB%AC%98%EC%82%AC" title="슈뢰딩거 묘사">슈뢰딩거 묘사</a>에서의 <a href="/wiki/%ED%9E%90%EB%B2%A0%EB%A5%B4%ED%8A%B8_%EA%B3%B5%EA%B0%84" title="힐베르트 공간">힐베르트 공간</a>의 <a href="/w/index.php?title=%EC%83%81%ED%83%9C_%EB%B2%A1%ED%84%B0&action=edit&redlink=1" class="new" title="상태 벡터 (없는 문서)">상태 벡터</a>이다. 이를 <a href="/wiki/%ED%8C%8C%EB%8F%99_%ED%95%A8%EC%88%98" title="파동 함수">파동 함수</a> <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 \psi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ψ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \psi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/45e5789e5d9c8f7c79744f43ecaaf8ba42a8553a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.513ex; height:2.509ex;" alt="{\displaystyle \psi }"></span>로 나타낼 수 있다. (<a href="/wiki/%ED%8C%8C%EB%8F%99_%ED%95%A8%EC%88%98" title="파동 함수">파동 함수</a>에 대한 해석은 <a href="/wiki/%EC%BD%94%ED%8E%9C%ED%95%98%EA%B2%90_%ED%95%B4%EC%84%9D" title="코펜하겐 해석">코펜하겐 해석</a>을 참조하라.) </p><p>해밀토니언 연산자 <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 {\hat {H}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>H</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\hat {H}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6bb06de5217295d7fbdbf68fb9c5309a513fc99e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.064ex; height:2.843ex;" alt="{\displaystyle {\hat {H}}}"></span>는 보통 미분 연산자이다. 예를 들어, 퍼텐셜 <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 V(\mathbf {x} ,t)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>V</mi> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">x</mi> </mrow> <mo>,</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V(\mathbf {x} ,t)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/738d924bdd43328ac8f2edaa7fa5b1c6f05ffd1a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.881ex; height:2.843ex;" alt="{\displaystyle V(\mathbf {x} ,t)}"></span> 속에 있는, 질량이 <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 m}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>m</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle m}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0a07d98bb302f3856cbabc47b2b9016692e3f7bc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.04ex; height:1.676ex;" alt="{\displaystyle m}"></span>인 비상대론적 입자의 경우 해밀토니언은 다음과 같은 2차 미분 연산자이다. </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 {\hat {H}}=-{\frac {\hbar ^{2}}{2m}}\nabla ^{2}+V(\mathbf {x} ,t)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>H</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mo>=</mo> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi class="MJX-variant">ℏ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mrow> <mn>2</mn> <mi>m</mi> </mrow> </mfrac> </mrow> <msup> <mi mathvariant="normal">∇</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mi>V</mi> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">x</mi> </mrow> <mo>,</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\hat {H}}=-{\frac {\hbar ^{2}}{2m}}\nabla ^{2}+V(\mathbf {x} ,t)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/53c3be3c42c1d8a4058c4ff7cc8003d281c65ae5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:23.721ex; height:5.676ex;" alt="{\displaystyle {\hat {H}}=-{\frac {\hbar ^{2}}{2m}}\nabla ^{2}+V(\mathbf {x} ,t)}"></span></dd></dl> <p>즉, 슈뢰딩거 방정식은 다음과 같은 2차 편미분 방정식이 된다. </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 i\hbar {\frac {\partial }{\partial t}}\psi (\mathbf {x} ,t)=\left(-{\frac {\hbar ^{2}}{2m}}\nabla ^{2}+V(\mathbf {x} ,t)\right)\psi (\mathbf {x} ,t)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>i</mi> <mi class="MJX-variant">ℏ</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi mathvariant="normal">∂</mi> <mrow> <mi mathvariant="normal">∂</mi> <mi>t</mi> </mrow> </mfrac> </mrow> <mi>ψ</mi> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">x</mi> </mrow> <mo>,</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mrow> <mo>(</mo> <mrow> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi class="MJX-variant">ℏ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mrow> <mn>2</mn> <mi>m</mi> </mrow> </mfrac> </mrow> <msup> <mi mathvariant="normal">∇</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mi>V</mi> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">x</mi> </mrow> <mo>,</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> <mo>)</mo> </mrow> <mi>ψ</mi> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">x</mi> </mrow> <mo>,</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle i\hbar {\frac {\partial }{\partial t}}\psi (\mathbf {x} ,t)=\left(-{\frac {\hbar ^{2}}{2m}}\nabla ^{2}+V(\mathbf {x} ,t)\right)\psi (\mathbf {x} ,t)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/09d70bbc2105f60538187e6bad7a6bd97132a447" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:43.782ex; height:6.343ex;" alt="{\displaystyle i\hbar {\frac {\partial }{\partial t}}\psi (\mathbf {x} ,t)=\left(-{\frac {\hbar ^{2}}{2m}}\nabla ^{2}+V(\mathbf {x} ,t)\right)\psi (\mathbf {x} ,t)}"></span></dd></dl> <div class="mw-heading mw-heading2"><h2 id="라그랑지언과_이차_양자화"><span id=".EB.9D.BC.EA.B7.B8.EB.9E.91.EC.A7.80.EC.96.B8.EA.B3.BC_.EC.9D.B4.EC.B0.A8_.EC.96.91.EC.9E.90.ED.99.94"></span>라그랑지언과 이차 양자화</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%EC%8A%88%EB%A2%B0%EB%94%A9%EA%B1%B0_%EB%B0%A9%EC%A0%95%EC%8B%9D&action=edit&section=2" title="부분 편집: 라그랑지언과 이차 양자화"><span>편집</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>슈뢰딩거 방정식은 다음과 같은 <a href="/wiki/%EB%9D%BC%EA%B7%B8%EB%9E%91%EC%A7%80%EC%96%B8" title="라그랑지언">라그랑지언</a>으로부터 유도할 수 있다. </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 {\mathcal {L}}=\psi ^{*}\left(i\hbar {\frac {\partial }{\partial t}}-{\hat {H}}\right)\psi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">L</mi> </mrow> </mrow> <mo>=</mo> <msup> <mi>ψ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msup> <mrow> <mo>(</mo> <mrow> <mi>i</mi> <mi class="MJX-variant">ℏ</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi mathvariant="normal">∂</mi> <mrow> <mi mathvariant="normal">∂</mi> <mi>t</mi> </mrow> </mfrac> </mrow> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>H</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> </mrow> <mo>)</mo> </mrow> <mi>ψ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {L}}=\psi ^{*}\left(i\hbar {\frac {\partial }{\partial t}}-{\hat {H}}\right)\psi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1a4d7b8a382dd656cc9d942cfaee97a2ff1eeb9e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:22.985ex; height:6.176ex;" alt="{\displaystyle {\mathcal {L}}=\psi ^{*}\left(i\hbar {\frac {\partial }{\partial t}}-{\hat {H}}\right)\psi }"></span></dd></dl> <p>예를 들어, 퍼텐셜 <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 V(\mathbf {x} ,t)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>V</mi> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">x</mi> </mrow> <mo>,</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V(\mathbf {x} ,t)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/738d924bdd43328ac8f2edaa7fa5b1c6f05ffd1a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.881ex; height:2.843ex;" alt="{\displaystyle V(\mathbf {x} ,t)}"></span> 속에 있는, 질량이 <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 m}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>m</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle m}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0a07d98bb302f3856cbabc47b2b9016692e3f7bc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.04ex; height:1.676ex;" alt="{\displaystyle m}"></span>인 비상대론적 입자의 경우 슈뢰딩거 라그랑지언은 다음과 같다. </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 {\mathcal {L}}=\psi ^{*}\left(i\hbar {\frac {\partial }{\partial t}}+{\frac {1}{2m}}\nabla ^{2}-V\right)\psi \sim \psi ^{*}i\hbar {\frac {\partial }{\partial t}}\psi -{\frac {1}{2m}}({\boldsymbol {\nabla }}\psi )^{2}-V|\psi |^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">L</mi> </mrow> </mrow> <mo>=</mo> <msup> <mi>ψ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msup> <mrow> <mo>(</mo> <mrow> <mi>i</mi> <mi class="MJX-variant">ℏ</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi mathvariant="normal">∂</mi> <mrow> <mi mathvariant="normal">∂</mi> <mi>t</mi> </mrow> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mn>2</mn> <mi>m</mi> </mrow> </mfrac> </mrow> <msup> <mi mathvariant="normal">∇</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <mi>V</mi> </mrow> <mo>)</mo> </mrow> <mi>ψ</mi> <mo>∼</mo> <msup> <mi>ψ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msup> <mi>i</mi> <mi class="MJX-variant">ℏ</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi mathvariant="normal">∂</mi> <mrow> <mi mathvariant="normal">∂</mi> <mi>t</mi> </mrow> </mfrac> </mrow> <mi>ψ</mi> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mn>2</mn> <mi>m</mi> </mrow> </mfrac> </mrow> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">∇</mi> </mrow> <mi>ψ</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>ψ</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {L}}=\psi ^{*}\left(i\hbar {\frac {\partial }{\partial t}}+{\frac {1}{2m}}\nabla ^{2}-V\right)\psi \sim \psi ^{*}i\hbar {\frac {\partial }{\partial t}}\psi -{\frac {1}{2m}}({\boldsymbol {\nabla }}\psi )^{2}-V|\psi |^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e260cf8c81183de57d3ed3b9c6e3d23663efb30b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:66.831ex; height:6.176ex;" alt="{\displaystyle {\mathcal {L}}=\psi ^{*}\left(i\hbar {\frac {\partial }{\partial t}}+{\frac {1}{2m}}\nabla ^{2}-V\right)\psi \sim \psi ^{*}i\hbar {\frac {\partial }{\partial t}}\psi -{\frac {1}{2m}}({\boldsymbol {\nabla }}\psi )^{2}-V|\psi |^{2}}"></span></dd></dl> <p>여기서 두 번째 표현은 전미분항(total derivative)을 무시하고 쓴 것이다. </p><p>이 라그랑지언을 고전적 가환 또는 <a href="/wiki/%EB%B0%98%EA%B0%80%ED%99%98%EC%88%98" title="반가환수">반가환</a> 장의 라그랑지언으로 여겨, <a href="/wiki/%EC%96%91%EC%9E%90%EC%9E%A5%EB%A1%A0" title="양자장론">양자장론</a>으로 이차 양자화시킬 수 있다. 이 경우, 외부 배경장 속에서 움직이는, 임의의 수의 비상대론적 보손 또는 페르미온을 나타내는 양자장론을 얻는다. 또한, 이 경우 비선형 상호작용항을 추가할 수 있다. 예를 들어, <a href="/wiki/%EA%B7%B8%EB%A1%9C%EC%8A%A4-%ED%94%BC%ED%83%80%EC%98%99%EC%8A%A4%ED%82%A4_%EB%B0%A9%EC%A0%95%EC%8B%9D" title="그로스-피타옙스키 방정식">그로스-피타옙스키 방정식</a>이 이러한 꼴이다. </p> <div class="mw-heading mw-heading2"><h2 id="역사"><span id=".EC.97.AD.EC.82.AC"></span>역사</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%EC%8A%88%EB%A2%B0%EB%94%A9%EA%B1%B0_%EB%B0%A9%EC%A0%95%EC%8B%9D&action=edit&section=3" title="부분 편집: 역사"><span>편집</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>1905년, <a href="/wiki/%EC%95%8C%EB%B2%A0%EB%A5%B4%ED%8A%B8_%EC%95%84%EC%9D%B8%EC%8A%88%ED%83%80%EC%9D%B8" title="알베르트 아인슈타인">알베르트 아인슈타인</a>은 <a href="/wiki/%EA%B4%91%EC%A0%84_%ED%9A%A8%EA%B3%BC" title="광전 효과">광전 효과</a>를 설명하기 위해서 <a href="/wiki/%EA%B4%91%EC%9E%90" title="광자">광자</a>의 <a href="/wiki/%EC%97%90%EB%84%88%EC%A7%80" title="에너지">에너지</a> E와 <a href="/wiki/%EC%A7%84%EB%8F%99%EC%88%98" title="진동수">진동수</a> ν 및 <a href="/wiki/%ED%94%8C%EB%9E%91%ED%81%AC_%EC%83%81%EC%88%98" title="플랑크 상수">플랑크 상수</a> h 사이의 관계를 </p> <dl><dd><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=h\nu }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>E</mi> <mo>=</mo> <mi>h</mi> <mi>ν</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E=h\nu }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c6c0386dc6d9530519404f95570fcc8548ed2326" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:7.445ex; height:2.176ex;" alt="{\displaystyle E=h\nu }"></span></dd></dl></dd></dl> <p>로 나타내었다. 1924년 <a href="/wiki/%EB%A3%A8%EC%9D%B4_%EB%93%9C_%EB%B8%8C%EB%A1%9C%EC%9D%B4" title="루이 드 브로이">루이 드 브로이</a>는 광자 뿐만 아니라 모든 입자가 대응되는 파동함수 <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 \psi \;}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ψ</mi> <mspace width="thickmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \psi \;}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1cd15010487ca1d8d4900f51eb7f49e785859255" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.158ex; height:2.509ex;" alt="{\displaystyle \psi \;}"></span>를 가진다는 <a href="/w/index.php?title=%EB%93%9C_%EB%B8%8C%EB%A1%9C%EC%9D%B4_%EA%B0%80%EC%84%A4&action=edit&redlink=1" class="new" title="드 브로이 가설 (없는 문서)">드 브로이 가설</a>을 발표하고, 파동의 파장 λ와 입자의 운동량 p에 대해 </p> <dl><dd><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 p=h/\lambda }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>p</mi> <mo>=</mo> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>λ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p=h/\lambda }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3f76ec3b598cf22f9742c127f9be31661ab06f6d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; margin-left: -0.089ex; width:8.214ex; height:2.843ex;" alt="{\displaystyle p=h/\lambda }"></span></dd></dl></dd></dl> <p>의 관계식을 제안했으며, 이 관계식이 특수상대론 및 위의 아인슈타인이 제안한 식과 일관됨을 보였다. 즉, E = hν는 광자 뿐만 아니라 모든 입자에 대해 성립한다는 것이다. </p><p>위 식들을 <a href="/wiki/%EA%B0%81%EC%A7%84%EB%8F%99%EC%88%98" title="각진동수">각진동수</a> <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 \omega =2\pi \nu \;}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ω</mi> <mo>=</mo> <mn>2</mn> <mi>π</mi> <mi>ν</mi> <mspace width="thickmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \omega =2\pi \nu \;}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6f84ceff6b6d714af867a153b7df47e6cdaf42fa" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:8.916ex; height:2.176ex;" alt="{\displaystyle \omega =2\pi \nu \;}"></span>와 <a href="/wiki/%ED%8C%8C%EC%88%98" title="파수">파수</a> <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=2\pi /\lambda \;}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>k</mi> <mo>=</mo> <mn>2</mn> <mi>π</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>λ</mi> <mspace width="thickmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle k=2\pi /\lambda \;}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b35033f8f2c6f20dbd39d8d18306d2fc044777dc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:9.967ex; height:2.843ex;" alt="{\displaystyle k=2\pi /\lambda \;}"></span> 및 <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 \hbar =h/2\pi \;}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi class="MJX-variant">ℏ</mi> <mo>=</mo> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> <mi>π</mi> <mspace width="thickmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \hbar =h/2\pi \;}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1e492b4692ff2436916e98e135d4705f79c61275" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:10.046ex; height:2.843ex;" alt="{\displaystyle \hbar =h/2\pi \;}"></span>를 이용해 표현하면, </p> <dl><dd><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=\hbar \omega }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>E</mi> <mo>=</mo> <mi class="MJX-variant">ℏ</mi> <mi>ω</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E=\hbar \omega }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fb16565f02349106457258633097e0d0414a8e2d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:7.626ex; height:2.176ex;" alt="{\displaystyle E=\hbar \omega }"></span> 및</dd></dl></dd></dl> <p><b>p</b>와 <b>k</b>를 <a href="/wiki/%EB%B2%A1%ED%84%B0_(%EB%AC%BC%EB%A6%AC)" class="mw-redirect" title="벡터 (물리)">벡터</a>로 표현하면 </p> <dl><dd><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 \mathbf {p} =\hbar \mathbf {k} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">p</mi> </mrow> <mo>=</mo> <mi class="MJX-variant">ℏ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">k</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {p} =\hbar \mathbf {k} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/95e73faf974069648fc56ca99c29c35950e6819c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:7.301ex; height:2.509ex;" alt="{\displaystyle \mathbf {p} =\hbar \mathbf {k} }"></span></dd></dl></dd></dl> <p><a href="/wiki/%EC%97%90%EB%A5%B4%EB%B9%88_%EC%8A%88%EB%A2%B0%EB%94%A9%EA%B1%B0" title="에르빈 슈뢰딩거">에르빈 슈뢰딩거</a>는 슈뢰딩거 방정식을 1925년 발표하였다.<sup id="cite_ref-Schrödinger25_1-1" class="reference"><a href="#cite_note-Schrödinger25-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> 슈뢰딩거는 <a href="/wiki/%ED%8F%89%EB%A9%B4%ED%8C%8C" title="평면파">평면파</a>의 <a href="/w/index.php?title=%EC%9C%84%EC%83%81_(%ED%8C%8C%EB%8F%99)&action=edit&redlink=1" class="new" title="위상 (파동) (없는 문서)">위상</a>을 <a href="/w/index.php?title=%EB%B3%B5%EC%86%8C&action=edit&redlink=1" class="new" title="복소 (없는 문서)">복소</a> <a href="/w/index.php?title=%EC%9C%84%EC%83%81%EC%9D%B8%EC%9E%90&action=edit&redlink=1" class="new" title="위상인자 (없는 문서)">위상인자</a>로 나타내었다. </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 \psi (\mathbf {x} ,t)=Ae^{i(\mathbf {k} \cdot \mathbf {x} -\omega t)}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ψ</mi> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">x</mi> </mrow> <mo>,</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>A</mi> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">k</mi> </mrow> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">x</mi> </mrow> <mo>−</mo> <mi>ω</mi> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \psi (\mathbf {x} ,t)=Ae^{i(\mathbf {k} \cdot \mathbf {x} -\omega t)}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/304e6917b9cfd5d622f892a36e126d3aee93cb5b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:19.958ex; height:3.343ex;" alt="{\displaystyle \psi (\mathbf {x} ,t)=Ae^{i(\mathbf {k} \cdot \mathbf {x} -\omega t)}}"></span></dd></dl> <p>그리고 그는 </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 {\frac {\partial }{\partial t}}\psi =-i\omega \psi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi mathvariant="normal">∂</mi> <mrow> <mi mathvariant="normal">∂</mi> <mi>t</mi> </mrow> </mfrac> </mrow> <mi>ψ</mi> <mo>=</mo> <mo>−</mo> <mi>i</mi> <mi>ω</mi> <mi>ψ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {\partial }{\partial t}}\psi =-i\omega \psi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/39b96ab65f699f53883b743b2bf5e2794cceaaae" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:13.175ex; height:5.509ex;" alt="{\displaystyle {\frac {\partial }{\partial t}}\psi =-i\omega \psi }"></span></dd></dl> <p>이므로 </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\psi =\hbar \omega \psi =i\hbar {\frac {\partial }{\partial t}}\psi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>E</mi> <mi>ψ</mi> <mo>=</mo> <mi class="MJX-variant">ℏ</mi> <mi>ω</mi> <mi>ψ</mi> <mo>=</mo> <mi>i</mi> <mi class="MJX-variant">ℏ</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi mathvariant="normal">∂</mi> <mrow> <mi mathvariant="normal">∂</mi> <mi>t</mi> </mrow> </mfrac> </mrow> <mi>ψ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E\psi =\hbar \omega \psi =i\hbar {\frac {\partial }{\partial t}}\psi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/97c81edc34de91b24fd04b2e74ebe962d4342a1f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:20.367ex; height:5.509ex;" alt="{\displaystyle E\psi =\hbar \omega \psi =i\hbar {\frac {\partial }{\partial t}}\psi }"></span></dd></dl> <p>이며, 마찬가지로 </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 {\frac {\partial }{\partial x}}\psi =ik_{x}\psi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi mathvariant="normal">∂</mi> <mrow> <mi mathvariant="normal">∂</mi> <mi>x</mi> </mrow> </mfrac> </mrow> <mi>ψ</mi> <mo>=</mo> <mi>i</mi> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msub> <mi>ψ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {\partial }{\partial x}}\psi =ik_{x}\psi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1946d83c03ef5a0369a9d21f84cff043e7b91e4c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:12.795ex; height:5.509ex;" alt="{\displaystyle {\frac {\partial }{\partial x}}\psi =ik_{x}\psi }"></span></dd></dl> <p>이므로 </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 p_{x}\psi =\hbar k_{x}\psi =-i\hbar {\frac {\partial }{\partial x}}\psi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msub> <mi>ψ</mi> <mo>=</mo> <mi class="MJX-variant">ℏ</mi> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msub> <mi>ψ</mi> <mo>=</mo> <mo>−</mo> <mi>i</mi> <mi class="MJX-variant">ℏ</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi mathvariant="normal">∂</mi> <mrow> <mi mathvariant="normal">∂</mi> <mi>x</mi> </mrow> </mfrac> </mrow> <mi>ψ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p_{x}\psi =\hbar k_{x}\psi =-i\hbar {\frac {\partial }{\partial x}}\psi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6e01303e15114c9e649a96ce55452b7d09dee9c2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; margin-left: -0.089ex; width:24.259ex; height:5.509ex;" alt="{\displaystyle p_{x}\psi =\hbar k_{x}\psi =-i\hbar {\frac {\partial }{\partial x}}\psi }"></span></dd></dl> <p>이고, 따라서 </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 p_{x}^{2}\psi =-\hbar ^{2}{\frac {\partial ^{2}}{\partial x^{2}}}\psi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mi>ψ</mi> <mo>=</mo> <mo>−</mo> <msup> <mi class="MJX-variant">ℏ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> <mi>ψ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p_{x}^{2}\psi =-\hbar ^{2}{\frac {\partial ^{2}}{\partial x^{2}}}\psi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a006af09a910c86a0c2165ee1383c3bbe89c5e05" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; margin-left: -0.089ex; width:17.279ex; height:6.009ex;" alt="{\displaystyle p_{x}^{2}\psi =-\hbar ^{2}{\frac {\partial ^{2}}{\partial x^{2}}}\psi }"></span></dd></dl> <p>및 각 방향의 부분들을 더하면 </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 p^{2}\psi =(p_{x}^{2}+p_{y}^{2}+p_{z}^{2})\psi =-\hbar ^{2}\left({\frac {\partial ^{2}}{\partial x^{2}}}+{\frac {\partial ^{2}}{\partial y^{2}}}+{\frac {\partial ^{2}}{\partial z^{2}}}\right)\psi =-\hbar ^{2}\nabla ^{2}\psi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi>ψ</mi> <mo>=</mo> <mo stretchy="false">(</mo> <msubsup> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mo>+</mo> <msubsup> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>y</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mo>+</mo> <msubsup> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>z</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mo stretchy="false">)</mo> <mi>ψ</mi> <mo>=</mo> <mo>−</mo> <msup> <mi class="MJX-variant">ℏ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mrow> <mo>(</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mi>z</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> <mi>ψ</mi> <mo>=</mo> <mo>−</mo> <msup> <mi class="MJX-variant">ℏ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mi mathvariant="normal">∇</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi>ψ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p^{2}\psi =(p_{x}^{2}+p_{y}^{2}+p_{z}^{2})\psi =-\hbar ^{2}\left({\frac {\partial ^{2}}{\partial x^{2}}}+{\frac {\partial ^{2}}{\partial y^{2}}}+{\frac {\partial ^{2}}{\partial z^{2}}}\right)\psi =-\hbar ^{2}\nabla ^{2}\psi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3f5d2d96c5801f09a1fd1c6daba7dfd9d86d85da" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; margin-left: -0.089ex; width:66.381ex; height:6.343ex;" alt="{\displaystyle p^{2}\psi =(p_{x}^{2}+p_{y}^{2}+p_{z}^{2})\psi =-\hbar ^{2}\left({\frac {\partial ^{2}}{\partial x^{2}}}+{\frac {\partial ^{2}}{\partial y^{2}}}+{\frac {\partial ^{2}}{\partial z^{2}}}\right)\psi =-\hbar ^{2}\nabla ^{2}\psi }"></span></dd></dl> <p>이 성립함을 알았다. 이제 이를 총 에너지 E와 <a href="/wiki/%EC%A7%88%EB%9F%89" title="질량">질량</a> m 및 <a href="/wiki/%EC%9C%84%EC%B9%98%EC%97%90%EB%84%88%EC%A7%80" class="mw-redirect" title="위치에너지">위치에너지</a>에 대한 <a href="/wiki/%EA%B3%A0%EC%A0%84%EC%97%AD%ED%95%99" title="고전역학">고전역학</a>적 공식 </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={\frac {p^{2}}{2m}}+V}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>E</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mrow> <mn>2</mn> <mi>m</mi> </mrow> </mfrac> </mrow> <mo>+</mo> <mi>V</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E={\frac {p^{2}}{2m}}+V}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/54a4d236168670313adfb55236184388827f8a73" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:13.541ex; height:5.676ex;" alt="{\displaystyle E={\frac {p^{2}}{2m}}+V}"></span> (단순히 총 에너지를 <a href="/wiki/%EC%9A%B4%EB%8F%99_%EC%97%90%EB%84%88%EC%A7%80" title="운동 에너지">운동 에너지</a>와 <a href="/wiki/%EC%9C%84%EC%B9%98_%EC%97%90%EB%84%88%EC%A7%80" title="위치 에너지">위치 에너지</a>의 합으로 나타낸 것)</dd></dl> <p>에 대입하여, 당시에 슈뢰딩거가 얻었던 위치에너지가 주어진 3차원 공간 상의 단일입자에 대한 공식에 도달한다. </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 i\hbar {\frac {\partial }{\partial t}}\psi =-{\frac {\hbar ^{2}}{2m}}\nabla ^{2}\psi +V\psi .}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>i</mi> <mi class="MJX-variant">ℏ</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi mathvariant="normal">∂</mi> <mrow> <mi mathvariant="normal">∂</mi> <mi>t</mi> </mrow> </mfrac> </mrow> <mi>ψ</mi> <mo>=</mo> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi class="MJX-variant">ℏ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mrow> <mn>2</mn> <mi>m</mi> </mrow> </mfrac> </mrow> <msup> <mi mathvariant="normal">∇</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi>ψ</mi> <mo>+</mo> <mi>V</mi> <mi>ψ</mi> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle i\hbar {\frac {\partial }{\partial t}}\psi =-{\frac {\hbar ^{2}}{2m}}\nabla ^{2}\psi +V\psi .}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a8337e22518371695afec421ceb3e7b819da2840" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:26.852ex; height:5.843ex;" alt="{\displaystyle i\hbar {\frac {\partial }{\partial t}}\psi =-{\frac {\hbar ^{2}}{2m}}\nabla ^{2}\psi +V\psi .}"></span></dd></dl> <div class="mw-heading mw-heading2"><h2 id="관련_방정식"><span id=".EA.B4.80.EB.A0.A8_.EB.B0.A9.EC.A0.95.EC.8B.9D"></span>관련 방정식</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%EC%8A%88%EB%A2%B0%EB%94%A9%EA%B1%B0_%EB%B0%A9%EC%A0%95%EC%8B%9D&action=edit&section=4" title="부분 편집: 관련 방정식"><span>편집</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>슈뢰딩거 방정식은 비상대론적이므로, <a href="/wiki/%ED%8A%B9%EC%88%98%EC%83%81%EB%8C%80%EB%A1%A0" class="mw-redirect" title="특수상대론">특수상대론</a>과 불합한다. 슈뢰딩거 방정식을 상대론적으로 일반화하면 <a href="/wiki/%EC%8A%A4%ED%95%80_(%EB%AC%BC%EB%A6%AC%ED%95%99)" title="스핀 (물리학)">스핀</a>에 따라 <a href="/wiki/%ED%81%B4%EB%9D%BC%EC%9D%B8_%EA%B3%A0%EB%93%A0_%EB%B0%A9%EC%A0%95%EC%8B%9D" class="mw-redirect" title="클라인 고든 방정식">클라인 고든 방정식</a>이나 <a href="/wiki/%EB%94%94%EB%9E%99_%EB%B0%A9%EC%A0%95%EC%8B%9D" title="디랙 방정식">디랙 방정식</a> 따위를 얻는다. 이들은 비상대론적인 <a href="/wiki/%EA%B7%B9%ED%95%9C" title="극한">극한</a>에서 슈뢰딩거 방정식으로 수렴한다. </p><p>또한, 슈뢰딩거 방정식에 비인 항을 추가할 수도 있다. 예를 들어, <a href="/wiki/%EC%9D%91%EC%A7%91%EB%AC%BC%EC%A7%88%EB%AC%BC%EB%A6%AC%ED%95%99" title="응집물질물리학">응집물질물리학</a>에서 <a href="/wiki/%EB%B3%B4%EC%8A%A4-%EC%95%84%EC%9D%B8%EC%8A%88%ED%83%80%EC%9D%B8_%EC%9D%91%EC%B6%95" title="보스-아인슈타인 응축">보스-아인슈타인 응축</a>을 나타내기 위해 사용하는 <a href="/wiki/%EA%B7%B8%EB%A1%9C%EC%8A%A4-%ED%94%BC%ED%83%80%EC%98%99%EC%8A%A4%ED%82%A4_%EB%B0%A9%EC%A0%95%EC%8B%9D" title="그로스-피타옙스키 방정식">그로스-피타옙스키 방정식</a>은 슈뢰딩거 방정식에 <a href="/wiki/%EC%82%AC%EC%8A%B9_%EC%83%81%ED%98%B8%EC%9E%91%EC%9A%A9" title="사승 상호작용">사승 상호작용</a>을 추가한 것이다. </p> <div class="mw-heading mw-heading2"><h2 id="같이_보기"><span id=".EA.B0.99.EC.9D.B4_.EB.B3.B4.EA.B8.B0"></span>같이 보기</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%EC%8A%88%EB%A2%B0%EB%94%A9%EA%B1%B0_%EB%B0%A9%EC%A0%95%EC%8B%9D&action=edit&section=5" title="부분 편집: 같이 보기"><span>편집</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/%ED%8C%8C%EB%8F%99_%EB%B0%A9%EC%A0%95%EC%8B%9D" title="파동 방정식">파동 방정식</a></li> <li><cite class="citation book">무어, 월터. 《슈뢰딩거의 삶》. 전대호 역. 사이언스북스.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=%EC%8A%88%EB%A2%B0%EB%94%A9%EA%B1%B0%EC%9D%98+%EC%82%B6&rft.pub=%EC%82%AC%EC%9D%B4%EC%96%B8%EC%8A%A4%EB%B6%81%EC%8A%A4&rft.aulast=%EB%AC%B4%EC%96%B4&rft.aufirst=%EC%9B%94%ED%84%B0&rfr_id=info%3Asid%2Fko.wikipedia.org%3A%EC%8A%88%EB%A2%B0%EB%94%A9%EA%B1%B0+%EB%B0%A9%EC%A0%95%EC%8B%9D" class="Z3988"><span style="display:none;"> </span></span></li></ul> <div class="mw-heading mw-heading2"><h2 id="각주"><span id=".EA.B0.81.EC.A3.BC"></span>각주</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%EC%8A%88%EB%A2%B0%EB%94%A9%EA%B1%B0_%EB%B0%A9%EC%A0%95%EC%8B%9D&action=edit&section=6" title="부분 편집: 각주"><span>편집</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r35556958">.mw-parser-output .reflist{font-size:90%;margin-bottom:0.5em;list-style-type:decimal}.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"><ol class="references"> <li id="cite_note-Schrödinger25-1"><span class="mw-cite-backlink">↑ <sup><a href="#cite_ref-Schrödinger25_1-0">가</a></sup> <sup><a href="#cite_ref-Schrödinger25_1-1">나</a></sup></span> <span class="reference-text"><cite class="citation journal"><a href="/wiki/%EC%97%90%EB%A5%B4%EB%B9%88_%EC%8A%88%EB%A2%B0%EB%94%A9%EA%B1%B0" title="에르빈 슈뢰딩거">Schrödinger, E.</a> (1926년 12월). “An undulatory theory of the mechanics of atoms and molecules”. 《Physical Review》 (영어) <b>28</b>: 1049. <a href="/wiki/%EB%94%94%EC%A7%80%ED%84%B8_%EA%B0%9D%EC%B2%B4_%EC%8B%9D%EB%B3%84%EC%9E%90" title="디지털 객체 식별자">doi</a>:<a rel="nofollow" class="external text" href="https://dx.doi.org/10.1103%2FPhysRev.28.1049">10.1103/PhysRev.28.1049</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physical+Review&rft.atitle=An+undulatory+theory+of+the+mechanics+of+atoms+and+molecules&rft.volume=28&rft.pages=1049&rft.date=1926-12&rft_id=info%3Adoi%2F10.1103%2FPhysRev.28.1049&rft.aulast=Schr%C3%B6dinger&rft.aufirst=E.&rfr_id=info%3Asid%2Fko.wikipedia.org%3A%EC%8A%88%EB%A2%B0%EB%94%A9%EA%B1%B0+%EB%B0%A9%EC%A0%95%EC%8B%9D" class="Z3988"><span style="display:none;"> </span></span></span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="외부_링크"><span id=".EC.99.B8.EB.B6.80_.EB.A7.81.ED.81.AC"></span>외부 링크</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%EC%8A%88%EB%A2%B0%EB%94%A9%EA%B1%B0_%EB%B0%A9%EC%A0%95%EC%8B%9D&action=edit&section=7" title="부분 편집: 외부 링크"><span>편집</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><cite class="citation web"><a rel="nofollow" class="external text" href="http://navercast.naver.com/contents.nhn?contents_id=1228">“슈뢰딩거 방정식”</a>. 《<a href="/wiki/%EB%84%A4%EC%9D%B4%EB%B2%84%EC%BA%90%EC%8A%A4%ED%8A%B8" title="네이버캐스트">네이버캐스트</a>》.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=%EB%84%A4%EC%9D%B4%EB%B2%84%EC%BA%90%EC%8A%A4%ED%8A%B8&rft.atitle=%EC%8A%88%EB%A2%B0%EB%94%A9%EA%B1%B0+%EB%B0%A9%EC%A0%95%EC%8B%9D&rft_id=http%3A%2F%2Fnavercast.naver.com%2Fcontents.nhn%3Fcontents_id%3D1228&rfr_id=info%3Asid%2Fko.wikipedia.org%3A%EC%8A%88%EB%A2%B0%EB%94%A9%EA%B1%B0+%EB%B0%A9%EC%A0%95%EC%8B%9D" class="Z3988"><span style="display:none;"> </span></span></li> <li><cite class="citation web"><a rel="nofollow" class="external text" href="https://encyclopediaofmath.org/wiki/Schr%C3%B6dinger_equation">“Schrödinger equation”</a>. 《Encyclopedia of Mathematics》 (영어). Springer-Verlag. 2001. <a href="/wiki/%EA%B5%AD%EC%A0%9C_%ED%91%9C%EC%A4%80_%EB%8F%84%EC%84%9C_%EB%B2%88%ED%98%B8" class="mw-redirect" title="국제 표준 도서 번호">ISBN</a> <a href="/wiki/%ED%8A%B9%EC%88%98:%EC%B1%85%EC%B0%BE%EA%B8%B0/978-1-55608-010-4" title="특수:책찾기/978-1-55608-010-4"><bdi>978-1-55608-010-4</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Encyclopedia+of+Mathematics&rft.atitle=Schr%C3%B6dinger+equation&rft.date=2001&rft.isbn=978-1-55608-010-4&rft_id=https%3A%2F%2Fencyclopediaofmath.org%2Fwiki%2FSchr%25C3%25B6dinger_equation&rfr_id=info%3Asid%2Fko.wikipedia.org%3A%EC%8A%88%EB%A2%B0%EB%94%A9%EA%B1%B0+%EB%B0%A9%EC%A0%95%EC%8B%9D" class="Z3988"><span style="display:none;"> </span></span></li> <li><cite class="citation web">Weisstein, Eric Wolfgang. <a rel="nofollow" class="external text" href="https://mathworld.wolfram.com/SchroedingerEquation.html">“Schrödinger equation”</a>. 《<a href="/wiki/%EB%A7%A4%EC%8A%A4%EC%9B%94%EB%93%9C" title="매스월드">Wolfram MathWorld</a>》 (영어). 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