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href=\"/wiki/%D0%92%D0%B8%D0%BA%D0%B8%D0%BF%D0%B5%D0%B4%D0%B8%D1%98%D0%B0:%D0%A3%D1%80%D0%B5%D0%B4%D1%83%D0%B2%D0%B0%D1%87%D0%BA%D0%B8_%D0%BD%D0%B0%D1%82%D0%BF%D1%80%D0%B5%D0%B2%D0%B0%D1%80%D0%B8\" title=\"Википедија:Уредувачки натпревари\"\u003Eуредувачки натпревар\u003C/a\u003E за \u003Cb\u003E\u003Ca href=\"/wiki/%D0%92%D0%B8%D0%BA%D0%B8%D0%BF%D0%B5%D0%B4%D0%B8%D1%98%D0%B0:%D0%A3%D1%80%D0%B5%D0%B4%D1%83%D0%B2%D0%B0%D1%87%D0%BA%D0%B8_%D0%BD%D0%B0%D1%82%D0%BF%D1%80%D0%B5%D0%B2%D0%B0%D1%80%D0%B8/%D0%A1%D1%80%D0%B5%D0%B4%D1%83%D0%B2%D0%B0%D1%9A%D0%B5_(2024)\" title=\"Википедија:Уредувачки натпревари/Средување (2024)\"\u003Eсредување на статии\u003C/a\u003E\u003C/b\u003E. Прочитајте ги правилата и вклучете се!\n\u003C/p\u003E\u003C/div\u003E\u003C/div\u003E\u003C/div\u003E\u003C/div\u003E\u003C/div\u003E";}}());</script></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="Мрежно место"> <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="Содржина" 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">Содржина</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">премести во страничникот</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">скриј</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">Почеток</div> </a> </li> <li id="toc-Историја" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Историја"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Историја</span> </div> </a> <ul id="toc-Историја-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Дефиниција" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Дефиниција"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Дефиниција</span> </div> </a> <button aria-controls="toc-Дефиниција-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Префрли на пододделот Дефиниција</span> </button> <ul id="toc-Дефиниција-sublist" class="vector-toc-list"> <li id="toc-Дефиниција_на_бранова_функција_преку_просторни_координати_и_време" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Дефиниција_на_бранова_функција_преку_просторни_координати_и_време"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1</span> <span>Дефиниција на бранова функција преку просторни координати и време</span> </div> </a> <ul id="toc-Дефиниција_на_бранова_функција_преку_просторни_координати_и_време-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Дефиниција_на_бранова_функција_преку_времето_и_координати_во_импулсниот_простор" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Дефиниција_на_бранова_функција_преку_времето_и_координати_во_импулсниот_простор"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2</span> <span>Дефиниција на бранова функција преку времето и координати во импулсниот простор</span> </div> </a> <ul id="toc-Дефиниција_на_бранова_функција_преку_времето_и_координати_во_импулсниот_простор-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Простор_на_бранови_функции" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Простор_на_бранови_функции"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Простор на бранови функции</span> </div> </a> <ul id="toc-Простор_на_бранови_функции-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Репрезентации" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Репрезентации"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Репрезентации</span> </div> </a> <button aria-controls="toc-Репрезентации-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Префрли на пододделот Репрезентации</span> </button> <ul id="toc-Репрезентации-sublist" class="vector-toc-list"> <li id="toc-Шредингерова_равенка" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Шредингерова_равенка"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.1</span> <span>Шредингерова равенка</span> </div> </a> <ul id="toc-Шредингерова_равенка-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Атом_на_водород" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Атом_на_водород"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.2</span> <span>Атом на водород</span> </div> </a> <ul id="toc-Атом_на_водород-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Поврзано" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Поврзано"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Поврзано</span> </div> </a> <ul id="toc-Поврзано-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Наводи" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Наводи"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Наводи</span> </div> </a> <ul id="toc-Наводи-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Литература" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Литература"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Литература</span> </div> </a> <ul id="toc-Литература-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Надворешни_врски" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Надворешни_врски"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>Надворешни врски</span> </div> </a> <ul id="toc-Надворешни_врски-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="Содржина" 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="Прик./скр. содржина" > <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">Прик./скр. содржина</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">Бранова функција</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="Појдете на статија на друг јазик. Достапно на 60 јазици" > <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-60" 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">60 јазици</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/Golffunksie" title="Golffunksie — африканс" lang="af" hreflang="af" data-title="Golffunksie" data-language-autonym="Afrikaans" data-language-local-name="африканс" 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/%D8%AF%D8%A7%D9%84%D8%A9_%D9%85%D9%88%D8%AC%D9%8A%D8%A9" title="دالة موجية — арапски" lang="ar" hreflang="ar" data-title="دالة موجية" data-language-autonym="العربية" data-language-local-name="арапски" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Funci%C3%B3n_d%27onda" title="Función d'onda — астурски" lang="ast" hreflang="ast" data-title="Función d'onda" data-language-autonym="Asturianu" data-language-local-name="астурски" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%A4%E0%A6%B0%E0%A6%99%E0%A7%8D%E0%A6%97_%E0%A6%AB%E0%A6%BE%E0%A6%82%E0%A6%B6%E0%A6%A8" title="তরঙ্গ ফাংশন — бенгалски" lang="bn" hreflang="bn" data-title="তরঙ্গ ফাংশন" data-language-autonym="বাংলা" data-language-local-name="бенгалски" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%A5%D0%B2%D0%B0%D0%BB%D0%B5%D0%B2%D0%B0%D1%8F_%D1%84%D1%83%D0%BD%D0%BA%D1%86%D1%8B%D1%8F" title="Хвалевая функцыя — белоруски" lang="be" hreflang="be" data-title="Хвалевая функцыя" data-language-autonym="Беларуская" data-language-local-name="белоруски" 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%92%D1%8A%D0%BB%D0%BD%D0%BE%D0%B2%D0%B0_%D1%84%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D1%8F" title="Вълнова функция — бугарски" lang="bg" hreflang="bg" data-title="Вълнова функция" data-language-autonym="Български" data-language-local-name="бугарски" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Talasna_funkcija" title="Talasna funkcija — босански" lang="bs" hreflang="bs" data-title="Talasna funkcija" data-language-autonym="Bosanski" data-language-local-name="босански" 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/Funci%C3%B3_d%27ona" title="Funció d'ona — каталонски" lang="ca" hreflang="ca" data-title="Funció d'ona" data-language-autonym="Català" data-language-local-name="каталонски" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%A5%D1%83%D0%BC%D0%BB%D0%B0_%D1%84%D1%83%D0%BD%D0%BA%D1%86%D0%B8" title="Хумла функци — чувашки" lang="cv" hreflang="cv" data-title="Хумла функци" data-language-autonym="Чӑвашла" data-language-local-name="чувашки" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Vlnov%C3%A1_funkce" title="Vlnová funkce — чешки" lang="cs" hreflang="cs" data-title="Vlnová funkce" data-language-autonym="Čeština" data-language-local-name="чешки" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/B%C3%B8lgefunktion" title="Bølgefunktion — дански" lang="da" hreflang="da" data-title="Bølgefunktion" data-language-autonym="Dansk" data-language-local-name="дански" 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/Wellenfunktion" title="Wellenfunktion — германски" lang="de" hreflang="de" data-title="Wellenfunktion" data-language-autonym="Deutsch" data-language-local-name="германски" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Lainefunktsioon" title="Lainefunktsioon — естонски" lang="et" hreflang="et" data-title="Lainefunktsioon" data-language-autonym="Eesti" data-language-local-name="естонски" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%9A%CF%85%CE%BC%CE%B1%CF%84%CE%BF%CF%83%CF%85%CE%BD%CE%AC%CF%81%CF%84%CE%B7%CF%83%CE%B7" title="Κυματοσυνάρτηση — грчки" lang="el" hreflang="el" data-title="Κυματοσυνάρτηση" data-language-autonym="Ελληνικά" data-language-local-name="грчки" 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/Wave_function" title="Wave function — англиски" lang="en" hreflang="en" data-title="Wave function" data-language-autonym="English" data-language-local-name="англиски" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Funci%C3%B3n_de_onda" title="Función de onda — шпански" lang="es" hreflang="es" data-title="Función de onda" data-language-autonym="Español" data-language-local-name="шпански" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Ondfunkcio" title="Ondfunkcio — есперанто" lang="eo" hreflang="eo" data-title="Ondfunkcio" data-language-autonym="Esperanto" data-language-local-name="есперанто" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Uhin-funtzio" title="Uhin-funtzio — баскиски" lang="eu" hreflang="eu" data-title="Uhin-funtzio" data-language-autonym="Euskara" data-language-local-name="баскиски" 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/%D8%AA%D8%A7%D8%A8%D8%B9_%D9%85%D9%88%D8%AC" title="تابع موج — персиски" lang="fa" hreflang="fa" data-title="تابع موج" data-language-autonym="فارسی" data-language-local-name="персиски" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Fonction_d%27onde" title="Fonction d'onde — француски" lang="fr" hreflang="fr" data-title="Fonction d'onde" data-language-autonym="Français" data-language-local-name="француски" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/Tonnfheidhm" title="Tonnfheidhm — ирски" lang="ga" hreflang="ga" data-title="Tonnfheidhm" data-language-autonym="Gaeilge" data-language-local-name="ирски" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Funci%C3%B3n_de_onda" title="Función de onda — галициски" lang="gl" hreflang="gl" data-title="Función de onda" data-language-autonym="Galego" data-language-local-name="галициски" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%ED%8C%8C%EB%8F%99_%ED%95%A8%EC%88%98" title="파동 함수 — корејски" lang="ko" hreflang="ko" data-title="파동 함수" data-language-autonym="한국어" data-language-local-name="корејски" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D4%B1%D5%AC%D5%AB%D6%84%D5%A1%D5%B5%D5%AB%D5%B6_%D6%86%D5%B8%D6%82%D5%B6%D5%AF%D6%81%D5%AB%D5%A1" title="Ալիքային ֆունկցիա — ерменски" lang="hy" hreflang="hy" data-title="Ալիքային ֆունկցիա" data-language-autonym="Հայերեն" data-language-local-name="ерменски" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Valna_funkcija" title="Valna funkcija — хрватски" lang="hr" hreflang="hr" data-title="Valna funkcija" data-language-autonym="Hrvatski" data-language-local-name="хрватски" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Fungsi_gelombang" title="Fungsi gelombang — индонезиски" lang="id" hreflang="id" data-title="Fungsi gelombang" data-language-autonym="Bahasa Indonesia" data-language-local-name="индонезиски" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Funzione_d%27onda" title="Funzione d'onda — италијански" lang="it" hreflang="it" data-title="Funzione d'onda" data-language-autonym="Italiano" data-language-local-name="италијански" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%A4%D7%95%D7%A0%D7%A7%D7%A6%D7%99%D7%99%D7%AA_%D7%92%D7%9C" title="פונקציית גל — хебрејски" lang="he" hreflang="he" data-title="פונקציית גל" data-language-autonym="עברית" data-language-local-name="хебрејски" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%A2%E1%83%90%E1%83%9A%E1%83%A6%E1%83%A3%E1%83%A0%E1%83%98_%E1%83%A4%E1%83%A3%E1%83%9C%E1%83%A5%E1%83%AA%E1%83%98%E1%83%90" title="ტალღური ფუნქცია — грузиски" lang="ka" hreflang="ka" data-title="ტალღური ფუნქცია" data-language-autonym="ქართული" data-language-local-name="грузиски" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%A2%D0%BE%D0%BB%D2%9B%D1%8B%D0%BD%D0%B4%D1%8B%D2%9B_%D1%84%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D1%8F" title="Толқындық функция — казашки" lang="kk" hreflang="kk" data-title="Толқындық функция" data-language-autonym="Қазақша" data-language-local-name="казашки" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-ky mw-list-item"><a href="https://ky.wikipedia.org/wiki/%D0%A2%D0%BE%D0%BB%D0%BA%D1%83%D0%BD_%D1%84%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D1%8F%D1%81%D1%8B" title="Толкун функциясы — киргиски" lang="ky" hreflang="ky" data-title="Толкун функциясы" data-language-autonym="Кыргызча" data-language-local-name="киргиски" class="interlanguage-link-target"><span>Кыргызча</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Bangin%C4%97_funkcija" title="Banginė funkcija — литвански" lang="lt" hreflang="lt" data-title="Banginė funkcija" data-language-autonym="Lietuvių" data-language-local-name="литвански" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Hull%C3%A1mf%C3%BCggv%C3%A9ny" title="Hullámfüggvény — унгарски" lang="hu" hreflang="hu" data-title="Hullámfüggvény" data-language-autonym="Magyar" data-language-local-name="унгарски" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-mn mw-list-item"><a href="https://mn.wikipedia.org/wiki/%D0%94%D0%BE%D0%BB%D0%B3%D0%B8%D0%BE%D0%BD%D1%8B_%D1%84%D1%83%D0%BD%D0%BA%D1%86" title="Долгионы функц — монголски" lang="mn" hreflang="mn" data-title="Долгионы функц" data-language-autonym="Монгол" data-language-local-name="монголски" class="interlanguage-link-target"><span>Монгол</span></a></li><li class="interlanguage-link interwiki-my mw-list-item"><a href="https://my.wikipedia.org/wiki/%E1%80%9C%E1%80%BE%E1%80%AD%E1%80%AF%E1%80%84%E1%80%BA%E1%80%B8%E1%80%9E%E1%80%9B%E1%80%AF%E1%80%95%E1%80%BA" title="လှိုင်းသရုပ် — бурмански" lang="my" hreflang="my" data-title="လှိုင်းသရုပ်" data-language-autonym="မြန်မာဘာသာ" data-language-local-name="бурмански" class="interlanguage-link-target"><span>မြန်မာဘာသာ</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Golffunctie" title="Golffunctie — холандски" lang="nl" hreflang="nl" data-title="Golffunctie" data-language-autonym="Nederlands" data-language-local-name="холандски" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E6%B3%A2%E5%8B%95%E9%96%A2%E6%95%B0" title="波動関数 — јапонски" lang="ja" hreflang="ja" data-title="波動関数" data-language-autonym="日本語" data-language-local-name="јапонски" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/B%C3%B8lgefunksjon" title="Bølgefunksjon — норвешки букмол" lang="nb" hreflang="nb" data-title="Bølgefunksjon" data-language-autonym="Norsk bokmål" data-language-local-name="норвешки букмол" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/B%C3%B8lgjefunksjon" title="Bølgjefunksjon — норвешки нинорск" lang="nn" hreflang="nn" data-title="Bølgjefunksjon" data-language-autonym="Norsk nynorsk" data-language-local-name="норвешки нинорск" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/To%CA%BBlqin_funksiyasi" title="Toʻlqin funksiyasi — узбечки" lang="uz" hreflang="uz" data-title="Toʻlqin funksiyasi" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="узбечки" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-pa mw-list-item"><a href="https://pa.wikipedia.org/wiki/%E0%A8%B5%E0%A9%87%E0%A8%B5_%E0%A8%AB%E0%A9%B0%E0%A8%95%E0%A8%B8%E0%A8%BC%E0%A8%A8" title="ਵੇਵ ਫੰਕਸ਼ਨ — пенџапски" lang="pa" hreflang="pa" data-title="ਵੇਵ ਫੰਕਸ਼ਨ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="пенџапски" 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/Funkcja_falowa" title="Funkcja falowa — полски" lang="pl" hreflang="pl" data-title="Funkcja falowa" data-language-autonym="Polski" data-language-local-name="полски" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Fun%C3%A7%C3%A3o_de_onda" title="Função de onda — португалски" lang="pt" hreflang="pt" data-title="Função de onda" data-language-autonym="Português" data-language-local-name="португалски" 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/Func%C8%9Bie_de_und%C4%83" title="Funcție de undă — романски" lang="ro" hreflang="ro" data-title="Funcție de undă" data-language-autonym="Română" data-language-local-name="романски" 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%92%D0%BE%D0%BB%D0%BD%D0%BE%D0%B2%D0%B0%D1%8F_%D1%84%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D1%8F" title="Волновая функция — руски" lang="ru" hreflang="ru" data-title="Волновая функция" data-language-autonym="Русский" data-language-local-name="руски" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Funksioni_i_val%C3%ABs" title="Funksioni i valës — албански" lang="sq" hreflang="sq" data-title="Funksioni i valës" data-language-autonym="Shqip" data-language-local-name="албански" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Wave_function" title="Wave function — Simple English" lang="en-simple" hreflang="en-simple" data-title="Wave function" 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/Vlnov%C3%A1_funkcia" title="Vlnová funkcia — словачки" lang="sk" hreflang="sk" data-title="Vlnová funkcia" data-language-autonym="Slovenčina" data-language-local-name="словачки" 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/Valovna_funkcija" title="Valovna funkcija — словенечки" lang="sl" hreflang="sl" data-title="Valovna funkcija" data-language-autonym="Slovenščina" data-language-local-name="словенечки" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/Talasna_funkcija" title="Talasna funkcija — српски" lang="sr" hreflang="sr" data-title="Talasna funkcija" data-language-autonym="Српски / srpski" data-language-local-name="српски" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Valna_funkcija" title="Valna funkcija — српскохрватски" lang="sh" hreflang="sh" data-title="Valna funkcija" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="српскохрватски" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Aaltofunktio" title="Aaltofunktio — фински" lang="fi" hreflang="fi" data-title="Aaltofunktio" data-language-autonym="Suomi" data-language-local-name="фински" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/V%C3%A5gfunktion" title="Vågfunktion — шведски" lang="sv" hreflang="sv" data-title="Vågfunktion" data-language-autonym="Svenska" data-language-local-name="шведски" 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%85%E0%AE%B2%E0%AF%88_%E0%AE%87%E0%AE%AF%E0%AE%95%E0%AF%8D%E0%AE%95%E0%AE%AE%E0%AF%8D" title="அலை இயக்கம் — тамилски" lang="ta" hreflang="ta" data-title="அலை இயக்கம்" data-language-autonym="தமிழ்" data-language-local-name="тамилски" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-tt mw-list-item"><a href="https://tt.wikipedia.org/wiki/%D0%94%D1%83%D0%BB%D0%BA%D1%8B%D0%BD%D1%87%D0%B0_%D1%84%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D1%8F" title="Дулкынча функция — татарски" lang="tt" hreflang="tt" data-title="Дулкынча функция" data-language-autonym="Татарча / tatarça" data-language-local-name="татарски" class="interlanguage-link-target"><span>Татарча / tatarça</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Dalga_fonksiyonu" title="Dalga fonksiyonu — турски" lang="tr" hreflang="tr" data-title="Dalga fonksiyonu" data-language-autonym="Türkçe" data-language-local-name="турски" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%A5%D0%B2%D0%B8%D0%BB%D1%8C%D0%BE%D0%B2%D0%B0_%D1%84%D1%83%D0%BD%D0%BA%D1%86%D1%96%D1%8F" title="Хвильова функція — украински" lang="uk" hreflang="uk" data-title="Хвильова функція" data-language-autonym="Українська" data-language-local-name="украински" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/H%C3%A0m_s%C3%B3ng" title="Hàm sóng — виетнамски" lang="vi" hreflang="vi" data-title="Hàm sóng" data-language-autonym="Tiếng Việt" data-language-local-name="виетнамски" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E6%B3%A2%E5%87%BD%E6%95%B8" title="波函數 — кантонски" lang="yue" hreflang="yue" data-title="波函數" data-language-autonym="粵語" data-language-local-name="кантонски" class="interlanguage-link-target"><span>粵語</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E6%B3%A2%E5%87%BD%E6%95%B0" title="波函数 — кинески" lang="zh" hreflang="zh" data-title="波函数" data-language-autonym="中文" data-language-local-name="кинески" class="interlanguage-link-target"><span>中文</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q2362761#sitelinks-wikipedia" title="Уредување на меѓујазични врски" class="wbc-editpage">Уреди врски</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div id="left-navigation"> <nav aria-label="Именски простори"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs 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</div> </div> <div id="bodyContent" class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">Од Википедија — слободната енциклопедија</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="mk" dir="ltr"><figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/%D0%9F%D0%BE%D0%B4%D0%B0%D1%82%D0%BE%D1%82%D0%B5%D0%BA%D0%B0:QuantumHarmonicOscillatorAnimation.gif" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/90/QuantumHarmonicOscillatorAnimation.gif/220px-QuantumHarmonicOscillatorAnimation.gif" decoding="async" width="220" height="274" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/9/90/QuantumHarmonicOscillatorAnimation.gif 1.5x" data-file-width="300" data-file-height="373" /></a><figcaption> Споредба на поимите <a href="/wiki/%D0%A5%D0%B0%D1%80%D0%BC%D0%BE%D0%BD%D0%B8%D1%81%D0%BA%D0%B8_%D1%82%D1%80%D0%B5%D0%BF%D0%B5%D1%80%D0%BD%D0%B8%D0%BA" title="Хармониски треперник">класичен</a> и <a href="/w/index.php?title=%D0%9A%D0%B2%D0%B0%D0%BD%D1%82%D0%B5%D0%BD_%D1%85%D0%B0%D1%80%D0%BC%D0%BE%D0%BD%D0%B8%D1%87%D0%B5%D0%BD_%D0%BE%D1%81%D1%86%D0%B8%D0%BB%D0%B0%D1%82%D0%BE%D1%80&action=edit&redlink=1" class="new" title="Квантен хармоничен осцилатор (страницата не постои)">квантен хармоничен осцилатор</a> за изолирани честички без спин. Описот на движењето кај класичните и квантните осцилатори е сосема различен. Класичниот осцилатор () е претставен како движење на честичка по патека. Квантниот осцилатор () нема точно дефинирана патека како што е познато во класичната физика. Наместо тоа, патеката на квантен осцилатор е опишана како бран; овде, вертикалната оска го прикажува реалниот (синиот) и имагинарниот дел од брановата функција (црвено). Анимациите () покажуваат четири различни решенија на стоен бран на <a href="/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">Шредингеровата равенка</a>. Анимациите () покажуваат две различни бранови функции кои се решенија на Шредингеровата равенка, но не се стојни бранови, туку се бранови кои пренесуваат енергија низ просторот.</figcaption></figure> <p><b>Бранова функција</b> — во <a href="/wiki/%D0%9A%D0%B2%D0%B0%D0%BD%D1%82%D0%BD%D0%B0_%D0%BC%D0%B5%D1%85%D0%B0%D0%BD%D0%B8%D0%BA%D0%B0" title="Квантна механика">квантната физика</a> се користи за да се опише <a href="/w/index.php?title=%D0%9A%D0%B2%D0%B0%D0%BD%D1%82%D0%BD%D0%B0_%D1%81%D0%BE%D1%81%D1%82%D0%BE%D1%98%D0%B1%D0%B0&action=edit&redlink=1" class="new" title="Квантна состојба (страницата не постои)">квантната состојба</a> на изолиран квантен систем. Брановата функција <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 mathvariant="normal">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/f5471531a3fe80741a839bc98d49fae862a6439a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.808ex; height:2.176ex;" alt="{\displaystyle \Psi }"></span> е <a href="/wiki/%D0%9A%D0%BE%D0%BC%D0%BF%D0%BB%D0%B5%D0%BA%D1%81%D0%BD%D0%B0_%D0%B0%D0%BD%D0%B0%D0%BB%D0%B8%D0%B7%D0%B0" title="Комплексна анализа">комплексна функција</a> која ја претставува амплитудата на <a href="/wiki/%D0%92%D0%B5%D1%80%D0%BE%D1%98%D0%B0%D1%82%D0%BD%D0%BE%D1%81%D1%82" title="Веројатност">веројатноста</a>, а квадратот на <a href="/wiki/%D0%90%D0%BF%D1%81%D0%BE%D0%BB%D1%83%D1%82%D0%BD%D0%B0_%D0%B2%D1%80%D0%B5%D0%B4%D0%BD%D0%BE%D1%81%D1%82" title="Апсолутна вредност">модулот</a> на брановата функција <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 |^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi mathvariant="normal">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 |\Psi |^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/682a3bc37b8f9eeba356ee232b5f33680d81c401" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.156ex; height:3.343ex;" alt="{\displaystyle |\Psi |^{2}}"></span> има значење на <a href="/wiki/%D0%92%D0%B5%D1%80%D0%BE%D1%98%D0%B0%D1%82%D0%BD%D0%BE%D1%81%D0%BD%D0%B0_%D1%80%D0%B0%D1%81%D0%BF%D1%80%D0%B5%D0%B4%D0%B5%D0%BB%D0%B1%D0%B0" title="Веројатносна распределба">густина на веројатност</a>. Ако брановата функција се дефинира како функција која зависи од просторните и временските координати, <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 ({\vec {x}},t)|^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi mathvariant="normal">Ψ</mi> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>x</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mo>,</mo> <mi>t</mi> <mo stretchy="false">)</mo> <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 |\Psi ({\vec {x}},t)|^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/da2c45952a751301290e3a82f774ce2078427607" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:9.169ex; height:3.343ex;" alt="{\displaystyle |\Psi ({\vec {x}},t)|^{2}}"></span> е <a href="/wiki/%D0%A0%D0%B5%D0%B0%D0%BB%D0%B5%D0%BD_%D0%B1%D1%80%D0%BE%D1%98" title="Реален број">реален број</a> и ја претставува <a href="/wiki/%D0%92%D0%B5%D1%80%D0%BE%D1%98%D0%B0%D1%82%D0%BD%D0%BE%D1%81%D1%82" title="Веројатност">веројатноста</a> честичката во времето <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 t}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>t</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle t}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/65658b7b223af9e1acc877d848888ecdb4466560" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.84ex; height:2.009ex;" alt="{\displaystyle t}"></span> да се најде на позиција <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 {\vec {x}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>x</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {x}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/db2dc6ced9cc3bc7e8b9f2707cbec033f6d3759c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.33ex; height:2.343ex;" alt="{\displaystyle {\vec {x}}}"></span>.<sup id="cite_ref-:0_1-0" class="reference"><a href="#cite_note-:0-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p><p>Најчестите симболи за брановата функција се грчките букви <span class="texhtml"><i>ψ</i></span> или <span class="texhtml">Ψ</span> (мала и голема <a href="/w/index.php?title=%D0%9F%D1%81%D0%B8_(%D0%B1%D1%83%D0%BA%D0%B2%D0%B0)&action=edit&redlink=1" class="new" title="Пси (буква) (страницата не постои)">пси</a>, соодветно). Самата бранова функција дефинирана како сложена функција <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 mathvariant="normal">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/f5471531a3fe80741a839bc98d49fae862a6439a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.808ex; height:2.176ex;" alt="{\displaystyle \Psi }"></span> не е <a href="/w/index.php?title=%D0%9E%D0%BF%D1%81%D0%B5%D1%80%D0%B2%D0%B0%D0%B1%D0%BB%D0%B0&action=edit&redlink=1" class="new" title="Опсервабла (страницата не постои)">опсервабилна</a> во физиката (не може да се мери директно), но квадратот на модулот на брановата функција <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 |^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi mathvariant="normal">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 |\Psi |^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/682a3bc37b8f9eeba356ee232b5f33680d81c401" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.156ex; height:3.343ex;" alt="{\displaystyle |\Psi |^{2}}"></span> и релативната фаза на брановата функција можат да се измерат. <a href="/wiki/%D0%9A%D0%BE%D1%80%D0%BF%D1%83%D1%81%D0%BA%D1%83%D0%BB%D0%B0%D1%80%D0%BD%D0%BE-%D0%B1%D1%80%D0%B0%D0%BD%D0%BE%D0%B2_%D0%B4%D1%83%D0%B0%D0%BB%D0%B8%D0%B7%D0%B0%D0%BC" title="Корпускуларно-бранов дуализам">Принципот на двојност</a> во квантната механика имплицира дека квантните системи можат еквивалентно да се опишат и како честички и како бранови (на пр. преку бранова функција). Двата описа се еквивалентни и обата се користат за опис на различни појави бидејќи едниот или другиот пристап е поедноставен и поинтуитивен за опишување на истите. </p><p>Брановата функција се наоѓа како решение на равенката зададена со квантните <a href="/w/index.php?title=%D0%A5%D0%B5%D1%80%D0%BC%D0%B8%D1%82%D1%81%D0%BA%D0%B0_%D0%BC%D0%B0%D1%82%D1%80%D0%B8%D1%86%D0%B0&action=edit&redlink=1" class="new" title="Хермитска матрица (страницата не постои)">хермитски оператори</a> (на пр., квантен Хамилтонов во <a href="/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">Шредингеровата равенка</a>). Со решавање на вакви равенки, добиваме <a href="/w/index.php?title=%D0%A1%D0%B2%D0%BE%D1%98%D1%81%D1%82%D0%B2%D0%B5%D0%BD%D0%B8_%D0%B2%D0%B5%D0%BA%D1%82%D0%BE%D1%80%D0%B8_%D0%B8_%D1%81%D0%B2%D0%BE%D1%98%D1%81%D1%82%D0%B2%D0%B5%D0%BD%D0%B8_%D0%B2%D1%80%D0%B5%D0%B4%D0%BD%D0%BE%D1%81%D1%82%D0%B8&action=edit&redlink=1" class="new" title="Својствени вектори и својствени вредности (страницата не постои)">својствени вредности</a> кои го претставуваат спектарот на можни резултати од мерењата и <a href="/w/index.php?title=%D0%A1%D0%B2%D0%BE%D1%98%D1%81%D1%82%D0%B2%D0%B5%D0%BD%D0%B8_%D0%B2%D0%B5%D0%BA%D1%82%D0%BE%D1%80%D0%B8_%D0%B8_%D1%81%D0%B2%D0%BE%D1%98%D1%81%D1%82%D0%B2%D0%B5%D0%BD%D0%B8_%D0%B2%D1%80%D0%B5%D0%B4%D0%BD%D0%BE%D1%81%D1%82%D0%B8&action=edit&redlink=1" class="new" title="Својствени вектори и својствени вредности (страницата не постои)">својствени вредности</a>својствени вектори кои претставуваат бранови функции на дадената равенка. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Историја"><span id=".D0.98.D1.81.D1.82.D0.BE.D1.80.D0.B8.D1.98.D0.B0"></span>Историја</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D0%91%D1%80%D0%B0%D0%BD%D0%BE%D0%B2%D0%B0_%D1%84%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D1%98%D0%B0&veaction=edit&section=1" title="Уреди го одделот „Историја“" class="mw-editsection-visualeditor"><span>уреди</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%D0%91%D1%80%D0%B0%D0%BD%D0%BE%D0%B2%D0%B0_%D1%84%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D1%98%D0%B0&action=edit&section=1" title="Уреди изворен код на одделот: Историја"><span>уреди извор</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/%D0%95%D1%80%D0%B2%D0%B8%D0%BD_%D0%A8%D1%80%D0%B5%D0%B4%D0%B8%D0%BD%D0%B3%D0%B5%D1%80" title="Ервин Шредингер">Ервин Шредингер</a> прв ја искористил брановата функција за да го опише микроскопското квантно однесување на честичките во <a href="/wiki/1926" title="1926">1926 година</a> кога направил аналогија на однесувањето на квантната честичка со однесувањето на <a href="/wiki/%D0%91%D1%80%D0%B0%D0%BD" title="Бран">брановите</a>. Во тоа време, Шредингер не сметал дека брановата функција е доволна за да опише вистински физички бран, но истата година <a href="/wiki/%D0%9C%D0%B0%D0%BA%D1%81_%D0%91%D0%BE%D1%80%D0%BD" title="Макс Борн">Макс Борн</a> предложил интерпретација на брановата функција преку густината на веројатноста, и оттогаш брановата функција, во смисла што се разбира денес, зазела фундаментално место за опишување на појави во <a href="/wiki/%D0%9A%D0%B2%D0%B0%D0%BD%D1%82%D0%BD%D0%B0_%D0%BC%D0%B5%D1%85%D0%B0%D0%BD%D0%B8%D0%BA%D0%B0" title="Квантна механика">квантната механика</a>.<sup id="cite_ref-:0_1-1" class="reference"><a href="#cite_note-:0-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Дефиниција"><span id=".D0.94.D0.B5.D1.84.D0.B8.D0.BD.D0.B8.D1.86.D0.B8.D1.98.D0.B0"></span>Дефиниција</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D0%91%D1%80%D0%B0%D0%BD%D0%BE%D0%B2%D0%B0_%D1%84%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D1%98%D0%B0&veaction=edit&section=2" title="Уреди го одделот „Дефиниција“" class="mw-editsection-visualeditor"><span>уреди</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%D0%91%D1%80%D0%B0%D0%BD%D0%BE%D0%B2%D0%B0_%D1%84%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D1%98%D0%B0&action=edit&section=2" title="Уреди изворен код на одделот: Дефиниција"><span>уреди извор</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Брановата функција е <a href="/wiki/%D0%A4%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D1%98%D0%B0_(%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0)" title="Функција (математика)">функција</a> зададена во однос на <a href="/w/index.php?title=%D0%A1%D1%82%D0%B5%D0%BF%D0%B5%D0%BD%D0%B8_%D0%BD%D0%B0_%D1%81%D0%BB%D0%BE%D0%B1%D0%BE%D0%B4%D0%B0_(%D0%BC%D0%B5%D1%85%D0%B0%D0%BD%D0%B8%D0%BA%D0%B0)&action=edit&redlink=1" class="new" title="Степени на слобода (механика) (страницата не постои)">степенот на слобода</a>, како што се просторните координати, временските координати, <a href="/wiki/%D0%A1%D0%BF%D0%B8%D0%BD_(%D1%84%D0%B8%D0%B7%D0%B8%D0%BA%D0%B0)" title="Спин (физика)">спин</a> честичките, итн. Кога за еден систем се избере максималното множество на комутациски опсервабли за степени на слобода, односно се изберат сите меѓусебно независни степени на слобода (просторната координата и спинот се независни степени на слобода, но импулсот и соодветната просторна координата не се меѓусебно независни степени на слобода, затоа што тие директно зависат еден од друг), за дадениот систем може да се дефинира бранова функција. </p><p>За даден систем, изборот на комутациските степени на слобода што треба да се користат не е единствен, и следствено и <a href="/w/index.php?title=%D0%94%D0%BE%D0%BC%D0%B5%D0%BD_(%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0)&action=edit&redlink=1" class="new" title="Домен (математика) (страницата не постои)">доменот</a> на брановата функција исто така не е единствен. На пример, брановата функција може да се запише како функција од просторните координати на честичките или како функција од импулсните координати на честичките во импулсниот простор. Овие две различни дефиниции на брановата функција даваат исти физички опсервабилни резултати и различно дефинираните бранови функции во реалниот и импулсниот простор се меѓусебно поврзани со <a href="/wiki/%D0%A4%D1%83%D1%80%D0%B8%D0%B5%D0%BE%D0%B2%D0%B0_%D1%82%D1%80%D0%B0%D0%BD%D1%81%D1%84%D0%BE%D1%80%D0%BC%D0%B0%D1%86%D0%B8%D1%98%D0%B0" class="mw-redirect" title="Фуриеова трансформација">Фуриевата трансформација</a>. </p><p>Некои честички, како што се <a href="/wiki/%D0%95%D0%BB%D0%B5%D0%BA%D1%82%D1%80%D0%BE%D0%BD" title="Електрон">електроните</a> и <a href="/wiki/%D0%A4%D0%BE%D1%82%D0%BE%D0%BD" title="Фотон">фотоните</a> <a href="/wiki/%D0%A1%D0%BF%D0%B8%D0%BD_(%D1%84%D0%B8%D0%B7%D0%B8%D0%BA%D0%B0)" title="Спин (физика)">, имаат спин кој</a> не е нула. Доколку спинот на честичката е значаен за набљудуваната појавашто сака да се опише, во дефиницијата на брановата функција за таа честичка, покрај просторните и/или временските координати, неопходно е да се вклучи спин како внатрешен, дискретен степен на слобода. Така, дополнително е можно да се вклучат и други степени на слобода, како што е <a href="/w/index.php?title=%D0%98%D0%B7%D0%BE%D1%81%D0%BF%D0%B8%D0%BD&action=edit&redlink=1" class="new" title="Изоспин (страницата не постои)">изоспин</a>, итн. Дискретните степени на слобода најчесто се претставени со <a href="/wiki/%D0%9C%D0%B0%D1%82%D1%80%D0%B8%D1%86%D0%B0_(%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0)" title="Матрица (математика)">матрични колони</a>. На пример. за спинот <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 s={\frac {1}{2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>s</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle s={\frac {1}{2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9897ecc029130e0845baa617516405d45c3aa01d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:6.188ex; height:5.176ex;" alt="{\displaystyle s={\frac {1}{2}}}"></span> се користи матрична колона <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 2\times 1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>2</mn> <mo>×</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 2\times 1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9206e2cc500de17a162b111d3c2cf61ec68c97a8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.165ex; height:2.176ex;" alt="{\displaystyle 2\times 1}"></span>, за спинот <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 s=1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>s</mi> <mo>=</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle s=1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bac386d8f227fb823cede9b3e33d706cad3ed306" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.351ex; height:2.176ex;" alt="{\displaystyle s=1}"></span>, се користи матрична колона <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 3\times 1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>3</mn> <mo>×</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 3\times 1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3a300ea5377e3d06f2a39ed9581e828776d279b3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.165ex; height:2.176ex;" alt="{\displaystyle 3\times 1}"></span>, итн. </p> <div class="mw-heading mw-heading3"><h3 id="Дефиниција_на_бранова_функција_преку_просторни_координати_и_време"><span id=".D0.94.D0.B5.D1.84.D0.B8.D0.BD.D0.B8.D1.86.D0.B8.D1.98.D0.B0_.D0.BD.D0.B0_.D0.B1.D1.80.D0.B0.D0.BD.D0.BE.D0.B2.D0.B0_.D1.84.D1.83.D0.BD.D0.BA.D1.86.D0.B8.D1.98.D0.B0_.D0.BF.D1.80.D0.B5.D0.BA.D1.83_.D0.BF.D1.80.D0.BE.D1.81.D1.82.D0.BE.D1.80.D0.BD.D0.B8_.D0.BA.D0.BE.D0.BE.D1.80.D0.B4.D0.B8.D0.BD.D0.B0.D1.82.D0.B8_.D0.B8_.D0.B2.D1.80.D0.B5.D0.BC.D0.B5"></span>Дефиниција на бранова функција преку просторни координати и време</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D0%91%D1%80%D0%B0%D0%BD%D0%BE%D0%B2%D0%B0_%D1%84%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D1%98%D0%B0&veaction=edit&section=3" title="Уреди го одделот „Дефиниција на бранова функција преку просторни координати и време“" class="mw-editsection-visualeditor"><span>уреди</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%D0%91%D1%80%D0%B0%D0%BD%D0%BE%D0%B2%D0%B0_%D1%84%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D1%98%D0%B0&action=edit&section=3" title="Уреди изворен код на одделот: Дефиниција на бранова функција преку просторни координати и време"><span>уреди извор</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Брановата функција за изолирана честичка која се движи со <a href="/wiki/%D0%A2%D0%B5%D0%BE%D1%80%D0%B8%D1%98%D0%B0_%D0%B7%D0%B0_%D1%80%D0%B5%D0%BB%D0%B0%D1%82%D0%B8%D0%B2%D0%BD%D0%BE%D1%81%D1%82%D0%B0" title="Теорија за релативноста">нерелативистичка брзина</a> чиј <a href="/wiki/%D0%A1%D0%BF%D0%B8%D0%BD_(%D1%84%D0%B8%D0%B7%D0%B8%D0%BA%D0%B0)" title="Спин (физика)">спин</a> не се зема предвид може да се претстави како функција само од просторните координати и времето како сложена функција на реални променливи <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 {\vec {x}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>x</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {x}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/db2dc6ced9cc3bc7e8b9f2707cbec033f6d3759c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.33ex; height:2.343ex;" alt="{\displaystyle {\vec {x}}}"></span> и <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 t}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>t</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle t}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/65658b7b223af9e1acc877d848888ecdb4466560" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.84ex; height:2.009ex;" alt="{\displaystyle t}"></span> : </p><p><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 ({\vec {x}},t)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Ψ</mi> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>x</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mo>,</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Psi ({\vec {x}},t)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/15cd0a4b77bf8aba0b07ef957e34d34956f8296b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.821ex; height:2.843ex;" alt="{\displaystyle \Psi ({\vec {x}},t)}"></span> </p><p>Квадратот на <a href="/wiki/%D0%90%D0%BF%D1%81%D0%BE%D0%BB%D1%83%D1%82%D0%BD%D0%B0_%D0%B2%D1%80%D0%B5%D0%B4%D0%BD%D0%BE%D1%81%D1%82" title="Апсолутна вредност">модулот</a> на брановата функција <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 ({\vec {x}},t)|^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi mathvariant="normal">Ψ</mi> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>x</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mo>,</mo> <mi>t</mi> <mo stretchy="false">)</mo> <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 |\Psi ({\vec {x}},t)|^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/da2c45952a751301290e3a82f774ce2078427607" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:9.169ex; height:3.343ex;" alt="{\displaystyle |\Psi ({\vec {x}},t)|^{2}}"></span> има значење на густина на веројатност: </p><p><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 ({\vec {x}},t)|^{2}=\Psi ^{*}({\vec {x}},t)\Psi ({\vec {x}},t)=\rho ({\vec {x}},t)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi mathvariant="normal">Ψ</mi> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>x</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mo>,</mo> <mi>t</mi> <mo stretchy="false">)</mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <msup> <mi mathvariant="normal">Ψ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msup> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>x</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mo>,</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mi mathvariant="normal">Ψ</mi> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>x</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mo>,</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>ρ</mi> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>x</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mo>,</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle |\Psi ({\vec {x}},t)|^{2}=\Psi ^{*}({\vec {x}},t)\Psi ({\vec {x}},t)=\rho ({\vec {x}},t)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8da0390fefcebc94565efcfd1f3f4b62e816847c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:36.276ex; height:3.343ex;" alt="{\displaystyle |\Psi ({\vec {x}},t)|^{2}=\Psi ^{*}({\vec {x}},t)\Psi ({\vec {x}},t)=\rho ({\vec {x}},t)}"></span> </p><p>Врз основа на стандардната дефиниција за веројатност, се наметнува условот за нормираност на брановата функција. Брановата функција мора да се нормира, така што вкупната веројатност да се најде честичка некаде во вселената е еднаква на 1: </p><p><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 \int _{-\infty }^{\infty }d{\vec {x}}\;|\Psi ({\vec {x}},t)|^{2}=1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mi mathvariant="normal">∞</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∞</mi> </mrow> </msubsup> <mi>d</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>x</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mspace width="thickmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi mathvariant="normal">Ψ</mi> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>x</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mo>,</mo> <mi>t</mi> <mo stretchy="false">)</mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \int _{-\infty }^{\infty }d{\vec {x}}\;|\Psi ({\vec {x}},t)|^{2}=1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e0c3b8c645af53797730d715b96b9a35e9b5d8d3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:21.454ex; height:6.009ex;" alt="{\displaystyle \int _{-\infty }^{\infty }d{\vec {x}}\;|\Psi ({\vec {x}},t)|^{2}=1}"></span> </p><p>На прашањето дали честичката е во одредена положба во одреден момент може да се одговори само преку информација за веројатноста дека честичката ќе биде во таа положба во тој момент. Веројатноста честичката која да се движи по една димензија во моментот <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 t}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>t</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle t}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/65658b7b223af9e1acc877d848888ecdb4466560" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.84ex; height:2.009ex;" alt="{\displaystyle t}"></span> да се најде во просторниот интервал помеѓу точките <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 a}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ffd2487510aa438433a2579450ab2b3d557e5edc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.23ex; height:1.676ex;" alt="{\displaystyle a}"></span> и <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 b}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>b</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle b}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f11423fbb2e967f986e36804a8ae4271734917c3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.998ex; height:2.176ex;" alt="{\displaystyle b}"></span> е даден со интегралот: </p><p><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_{a\leq x\leq b}(t)=\int _{a}^{b}dx\;|\Psi (x,t)|^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> <mo>≤</mo> <mi>x</mi> <mo>≤</mo> <mi>b</mi> </mrow> </msub> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>=</mo> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> </mrow> </msubsup> <mi>d</mi> <mi>x</mi> <mspace width="thickmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi mathvariant="normal">Ψ</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo>,</mo> <mi>t</mi> <mo stretchy="false">)</mo> <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 P_{a\leq x\leq b}(t)=\int _{a}^{b}dx\;|\Psi (x,t)|^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b082bc7fb593ecf54169597fcff4e57d6991dd6b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:28.692ex; height:6.343ex;" alt="{\displaystyle P_{a\leq x\leq b}(t)=\int _{a}^{b}dx\;|\Psi (x,t)|^{2}}"></span> </p> <div class="mw-heading mw-heading3"><h3 id="Дефиниција_на_бранова_функција_преку_времето_и_координати_во_импулсниот_простор"><span id=".D0.94.D0.B5.D1.84.D0.B8.D0.BD.D0.B8.D1.86.D0.B8.D1.98.D0.B0_.D0.BD.D0.B0_.D0.B1.D1.80.D0.B0.D0.BD.D0.BE.D0.B2.D0.B0_.D1.84.D1.83.D0.BD.D0.BA.D1.86.D0.B8.D1.98.D0.B0_.D0.BF.D1.80.D0.B5.D0.BA.D1.83_.D0.B2.D1.80.D0.B5.D0.BC.D0.B5.D1.82.D0.BE_.D0.B8_.D0.BA.D0.BE.D0.BE.D1.80.D0.B4.D0.B8.D0.BD.D0.B0.D1.82.D0.B8_.D0.B2.D0.BE_.D0.B8.D0.BC.D0.BF.D1.83.D0.BB.D1.81.D0.BD.D0.B8.D0.BE.D1.82_.D0.BF.D1.80.D0.BE.D1.81.D1.82.D0.BE.D1.80"></span>Дефиниција на бранова функција преку времето и координати во импулсниот простор</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D0%91%D1%80%D0%B0%D0%BD%D0%BE%D0%B2%D0%B0_%D1%84%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D1%98%D0%B0&veaction=edit&section=4" title="Уреди го одделот „Дефиниција на бранова функција преку времето и координати во импулсниот простор“" class="mw-editsection-visualeditor"><span>уреди</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%D0%91%D1%80%D0%B0%D0%BD%D0%BE%D0%B2%D0%B0_%D1%84%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D1%98%D0%B0&action=edit&section=4" title="Уреди изворен код на одделот: Дефиниција на бранова функција преку времето и координати во импулсниот простор"><span>уреди извор</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Брановата функција на честичката не мора да биде зададена преку просторните и временските координати. Еквивалентни физички резултати дава и дефиницијата на брановата функција преку импулси и времето како: </p><p><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 \Phi ({\vec {p}},t)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Φ</mi> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>p</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mo>,</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Phi ({\vec {p}},t)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f36122172a91c4cc960698f012d8e943a5eb8a8d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.686ex; height:2.843ex;" alt="{\displaystyle \Phi ({\vec {p}},t)}"></span> </p><p>На сличен начин се поставува условот за нормираност и слично квадратот на <a href="/wiki/%D0%90%D0%BF%D1%81%D0%BE%D0%BB%D1%83%D1%82%D0%BD%D0%B0_%D0%B2%D1%80%D0%B5%D0%B4%D0%BD%D0%BE%D1%81%D1%82" title="Апсолутна вредност">модулот</a> на брановата функција <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 |\Phi ({\vec {p}},t)|^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi mathvariant="normal">Φ</mi> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>p</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mo>,</mo> <mi>t</mi> <mo stretchy="false">)</mo> <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 |\Phi ({\vec {p}},t)|^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e40b1c8dbeb0c388bb7138f9e947f3e411b2ca0e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:9.034ex; height:3.343ex;" alt="{\displaystyle |\Phi ({\vec {p}},t)|^{2}}"></span> има значење на веројатност дека честичката во моментот <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 t}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>t</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle t}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/65658b7b223af9e1acc877d848888ecdb4466560" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.84ex; height:2.009ex;" alt="{\displaystyle t}"></span> поседува импулс <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 {\vec {p}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>p</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {p}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/84fee53c81592db54e0fe6c6f9eba002bb1dc74b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.089ex; width:1.415ex; height:2.676ex;" alt="{\displaystyle {\vec {p}}}"></span>. </p> <div class="mw-heading mw-heading2"><h2 id="Простор_на_бранови_функции"><span id=".D0.9F.D1.80.D0.BE.D1.81.D1.82.D0.BE.D1.80_.D0.BD.D0.B0_.D0.B1.D1.80.D0.B0.D0.BD.D0.BE.D0.B2.D0.B8_.D1.84.D1.83.D0.BD.D0.BA.D1.86.D0.B8.D0.B8"></span>Простор на бранови функции</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D0%91%D1%80%D0%B0%D0%BD%D0%BE%D0%B2%D0%B0_%D1%84%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D1%98%D0%B0&veaction=edit&section=5" title="Уреди го одделот „Простор на бранови функции“" class="mw-editsection-visualeditor"><span>уреди</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%D0%91%D1%80%D0%B0%D0%BD%D0%BE%D0%B2%D0%B0_%D1%84%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D1%98%D0%B0&action=edit&section=5" title="Уреди изворен код на одделот: Простор на бранови функции"><span>уреди извор</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Просторот на брановите функции во кој тие се дефинирани е <a href="/w/index.php?title=%D0%A5%D0%B8%D0%BB%D0%B1%D0%B5%D1%80%D1%82%D0%BE%D0%B2_%D0%BF%D1%80%D0%BE%D1%81%D1%82%D0%BE%D1%80&action=edit&redlink=1" class="new" title="Хилбертов простор (страницата не постои)">Хилбертов простор</a>. Брановите функции кои го претставуваат решението на <a href="/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">Шредингеровата равенка</a> задоволуваат: </p> <ul><li><a href="/w/index.php?title=%D0%A1%D1%83%D0%BF%D0%B5%D1%80%D0%BF%D0%BE%D0%B7%D0%B8%D1%86%D0%B8%D1%98%D0%B0&action=edit&redlink=1" class="new" title="Суперпозиција (страницата не постои)">својство на суперпозиција</a>: бидејќи <a href="/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">Шредингеровата равенка е</a> линеарна <a href="/wiki/%D0%94%D0%B8%D1%84%D0%B5%D1%80%D0%B5%D0%BD%D1%86%D0%B8%D1%98%D0%B0%D0%BB%D0%BD%D0%B0_%D1%80%D0%B0%D0%B2%D0%B5%D0%BD%D0%BA%D0%B0" title="Диференцијална равенка">диференцијална равенка</a>, ако функциите <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 _{1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi mathvariant="normal">Ψ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Psi _{1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ddcd58cf9c1c4dd1eb32a29c1e3abf425ec72600" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.862ex; height:2.509ex;" alt="{\displaystyle \Psi _{1}}"></span> и <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 _{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi mathvariant="normal">Ψ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Psi _{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1125553c0a026635c63ab2ad542b43174aca9bbe" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.862ex; height:2.509ex;" alt="{\displaystyle \Psi _{2}}"></span> се две различни решенија на Шредингеровата равенка, тогаш има и нивна линеарна комбинација <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 a\Psi _{1}+b\Psi _{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> <msub> <mi mathvariant="normal">Ψ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>+</mo> <mi>b</mi> <msub> <mi mathvariant="normal">Ψ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a\Psi _{1}+b\Psi _{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6ade04337a386009c17a0891ce5c8c33268706d7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:10.793ex; height:2.509ex;" alt="{\displaystyle a\Psi _{1}+b\Psi _{2}}"></span>, каде <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 a}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ffd2487510aa438433a2579450ab2b3d557e5edc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.23ex; height:1.676ex;" alt="{\displaystyle a}"></span> и <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 b}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>b</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle b}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f11423fbb2e967f986e36804a8ae4271734917c3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.998ex; height:2.176ex;" alt="{\displaystyle b}"></span> се комплексни броеви, решение на Шредингеровата равенка.</li> <li>дефинираност до константа. Ако <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 mathvariant="normal">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/f5471531a3fe80741a839bc98d49fae862a6439a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.808ex; height:2.176ex;" alt="{\displaystyle \Psi }"></span> е решението на <a href="/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">Шредингеровата равенка</a>, тогаш и <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 +C}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Ψ</mi> <mo>+</mo> <mi>C</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Psi +C}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7212090bd859ada25cad01acbe987a4fe82f3ad0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:6.415ex; height:2.343ex;" alt="{\displaystyle \Psi +C}"></span>, при што <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 C}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>C</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle C}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4fc55753007cd3c18576f7933f6f089196732029" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.766ex; height:2.176ex;" alt="{\displaystyle C}"></span> е произволна константа, решение на дадената равенка.</li></ul> <p><a href="/w/index.php?title=%D0%92%D0%BD%D0%B0%D1%82%D1%80%D0%B5%D1%88%D0%B5%D0%BD_%D0%BF%D1%80%D0%BE%D0%B8%D0%B7%D0%B2%D0%BE%D0%B4&action=edit&redlink=1" class="new" title="Внатрешен производ (страницата не постои)">Внатрешен производ</a> помеѓу две бранови функции: </p><p><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 \langle \Psi _{1}(x)|\Psi _{2}(x)\rangle =\int _{-\infty }^{+\infty }dx\;\Psi _{1}^{*}(x)\Psi _{2}(x)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo fence="false" stretchy="false">⟨</mo> <msub> <mi mathvariant="normal">Ψ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <msub> <mi mathvariant="normal">Ψ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo fence="false" stretchy="false">⟩</mo> <mo>=</mo> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mi mathvariant="normal">∞</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>+</mo> <mi mathvariant="normal">∞</mi> </mrow> </msubsup> <mi>d</mi> <mi>x</mi> <mspace width="thickmathspace" /> <msubsup> <mi mathvariant="normal">Ψ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msubsup> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <msub> <mi mathvariant="normal">Ψ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \langle \Psi _{1}(x)|\Psi _{2}(x)\rangle =\int _{-\infty }^{+\infty }dx\;\Psi _{1}^{*}(x)\Psi _{2}(x)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/60fb2e9a6b3a62e1156ea150fe89d70d9e5b8ee6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:38.756ex; height:6.176ex;" alt="{\displaystyle \langle \Psi _{1}(x)|\Psi _{2}(x)\rangle =\int _{-\infty }^{+\infty }dx\;\Psi _{1}^{*}(x)\Psi _{2}(x)}"></span> </p><p>е мерка за преклопување помеѓу соодветните физички состојби и има значење на веројатност за премин од состојбата опишана со брановата функција <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 _{1}(x)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi mathvariant="normal">Ψ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Psi _{1}(x)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cb8c09f693f32d237fcafede59a5c6b940931513" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.001ex; height:2.843ex;" alt="{\displaystyle \Psi _{1}(x)}"></span> во состојба опишана со брановата функција <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 _{2}(x)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi mathvariant="normal">Ψ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Psi _{2}(x)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/35eb880ab68bbb9690cb8036651aa3efbe23d8be" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.001ex; height:2.843ex;" alt="{\displaystyle \Psi _{2}(x)}"></span>, или обратно. </p> <div class="mw-heading mw-heading2"><h2 id="Репрезентации"><span id=".D0.A0.D0.B5.D0.BF.D1.80.D0.B5.D0.B7.D0.B5.D0.BD.D1.82.D0.B0.D1.86.D0.B8.D0.B8"></span>Репрезентации</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D0%91%D1%80%D0%B0%D0%BD%D0%BE%D0%B2%D0%B0_%D1%84%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D1%98%D0%B0&veaction=edit&section=6" title="Уреди го одделот „Репрезентации“" class="mw-editsection-visualeditor"><span>уреди</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%D0%91%D1%80%D0%B0%D0%BD%D0%BE%D0%B2%D0%B0_%D1%84%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D1%98%D0%B0&action=edit&section=6" title="Уреди изворен код на одделот: Репрезентации"><span>уреди извор</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Шредингерова_равенка"><span id=".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"></span>Шредингерова равенка</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D0%91%D1%80%D0%B0%D0%BD%D0%BE%D0%B2%D0%B0_%D1%84%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D1%98%D0%B0&veaction=edit&section=7" title="Уреди го одделот „Шредингерова равенка“" class="mw-editsection-visualeditor"><span>уреди</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%D0%91%D1%80%D0%B0%D0%BD%D0%BE%D0%B2%D0%B0_%D1%84%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D1%98%D0%B0&action=edit&section=7" title="Уреди изворен код на одделот: Шредингерова равенка"><span>уреди извор</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Брановата функција <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 mathvariant="normal">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/f5471531a3fe80741a839bc98d49fae862a6439a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.808ex; height:2.176ex;" alt="{\displaystyle \Psi }"></span> е решението на <a href="/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">Шредингеровата равенка</a>: </p><p><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 ={\hat {H}}\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 mathvariant="normal">Ψ</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>H</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mi mathvariant="normal">Ψ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle i\hbar {\frac {\partial }{\partial t}}\Psi ={\hat {H}}\Psi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a2cd929448cc3ac4835a3f10ef6a01a81f533e17" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:13.881ex; height:5.509ex;" alt="{\displaystyle i\hbar {\frac {\partial }{\partial t}}\Psi ={\hat {H}}\Psi }"></span> </p><p>кој ја опишува промената во системот како функција на времето. <a href="/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">Шредингеровата равенка</a> опишува како брановите функции еволуираат со текот на времето. Бидејќи Шредингеровата равенка е математички тип на <a href="/wiki/%D0%91%D1%80%D0%B0%D0%BD%D0%BE%D0%B2%D0%B0_%D1%80%D0%B0%D0%B2%D0%B5%D0%BD%D0%BA%D0%B0" title="Бранова равенка">бранова равенка</a>, нејзиното решение кое го претставува брановата функција <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 mathvariant="normal">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/f5471531a3fe80741a839bc98d49fae862a6439a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.808ex; height:2.176ex;" alt="{\displaystyle \Psi }"></span> квалитативно се однесува како и макроскопските <a href="/wiki/%D0%91%D1%80%D0%B0%D0%BD" title="Бран">бранови</a>, како што се водените бранови или брановите на жица.<i><sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup></i> </p> <div class="mw-heading mw-heading3"><h3 id="Атом_на_водород"><span id=".D0.90.D1.82.D0.BE.D0.BC_.D0.BD.D0.B0_.D0.B2.D0.BE.D0.B4.D0.BE.D1.80.D0.BE.D0.B4"></span>Атом на водород</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D0%91%D1%80%D0%B0%D0%BD%D0%BE%D0%B2%D0%B0_%D1%84%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D1%98%D0%B0&veaction=edit&section=8" title="Уреди го одделот „Атом на водород“" class="mw-editsection-visualeditor"><span>уреди</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%D0%91%D1%80%D0%B0%D0%BD%D0%BE%D0%B2%D0%B0_%D1%84%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D1%98%D0%B0&action=edit&section=8" title="Уреди изворен код на одделот: Атом на водород"><span>уреди извор</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/%D0%9F%D0%BE%D0%B4%D0%B0%D1%82%D0%BE%D1%82%D0%B5%D0%BA%D0%B0:Hydrogen_Density_Plots-ca.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d8/Hydrogen_Density_Plots-ca.png/220px-Hydrogen_Density_Plots-ca.png" decoding="async" width="220" height="200" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d8/Hydrogen_Density_Plots-ca.png/330px-Hydrogen_Density_Plots-ca.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/d8/Hydrogen_Density_Plots-ca.png/440px-Hydrogen_Density_Plots-ca.png 2x" data-file-width="2200" data-file-height="2000" /></a><figcaption> Електронска густина на веројатност <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 _{n\ell m}|^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <msub> <mi mathvariant="normal">Ψ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mi>ℓ</mi> <mi>m</mi> </mrow> </msub> <msup> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle |\Psi _{n\ell m}|^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4e8b4940c62863eaeca96e57bd1c9c3f4fca4d87" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:7.503ex; height:3.343ex;" alt="{\displaystyle |\Psi _{n\ell m}|^{2}}"></span> на различни <a href="/wiki/%D0%90%D1%82%D0%BE%D0%BC%D1%81%D0%BA%D0%B0_%D0%BE%D1%80%D0%B1%D0%B8%D1%82%D0%B0%D0%BB%D0%B0" title="Атомска орбитала">орбитали</a> кои ја градат целокупната бранова функција на атомот на водород како решение на <a href="/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">Шредингеровата равенка</a>.</figcaption></figure> <p>Решението на временско-независната Шредингерова равенка за атом на водород (не земајќи го предвид <a href="/wiki/%D0%A1%D0%BF%D0%B8%D0%BD_(%D1%84%D0%B8%D0%B7%D0%B8%D0%BA%D0%B0)" title="Спин (физика)">спинот на</a> атомот) е бранова функција која може да се изрази во однос на радијална функција која <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 R(r)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>R</mi> <mo stretchy="false">(</mo> <mi>r</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle R(r)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f7b97817d8756302ef44f910ec5e76346e8d4f4d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.622ex; height:2.843ex;" alt="{\displaystyle R(r)}"></span> што зависи само од радијалните координати <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 r}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>r</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0d1ecb613aa2984f0576f70f86650b7c2a132538" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.049ex; height:1.676ex;" alt="{\displaystyle r}"></span> и <a href="/w/index.php?title=%D0%A1%D1%84%D0%B5%D1%80%D0%BD%D0%B8_%D1%85%D0%B0%D1%80%D0%BC%D0%BE%D0%BD%D0%B8%D1%86%D0%B8&action=edit&redlink=1" class="new" title="Сферни хармоници (страницата не постои)">сферниот хармоник</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 Y_{\ell }^{m}\!(\theta ,\phi )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mi>Y</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>ℓ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> </mrow> </msubsup> <mspace width="negativethinmathspace" /> <mo stretchy="false">(</mo> <mi>θ</mi> <mo>,</mo> <mi>ϕ</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Y_{\ell }^{m}\!(\theta ,\phi )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/998184584baea432813102223878a03f5b00d42c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:8.507ex; height:3.009ex;" alt="{\displaystyle Y_{\ell }^{m}\!(\theta ,\phi )}"></span> што зависи од аголните координати <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 \theta }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>θ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \theta }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6e5ab2664b422d53eb0c7df3b87e1360d75ad9af" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.09ex; height:2.176ex;" alt="{\displaystyle \theta }"></span> и <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 \phi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ϕ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \phi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/72b1f30316670aee6270a28334bdf4f5072cdde4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.385ex; height:2.509ex;" alt="{\displaystyle \phi }"></span>. </p><p><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 _{n\ell m}(r,\theta ,\phi )=R(r)\,\,Y_{\ell }^{m}\!(\theta ,\phi )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi mathvariant="normal">Ψ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mi>ℓ</mi> <mi>m</mi> </mrow> </msub> <mo stretchy="false">(</mo> <mi>r</mi> <mo>,</mo> <mi>θ</mi> <mo>,</mo> <mi>ϕ</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>R</mi> <mo stretchy="false">(</mo> <mi>r</mi> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> <mspace width="thinmathspace" /> <msubsup> <mi>Y</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>ℓ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> </mrow> </msubsup> <mspace width="negativethinmathspace" /> <mo stretchy="false">(</mo> <mi>θ</mi> <mo>,</mo> <mi>ϕ</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Psi _{n\ell m}(r,\theta ,\phi )=R(r)\,\,Y_{\ell }^{m}\!(\theta ,\phi )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fd33b6d9041b12d6ccd521e4c1137ec7a23ba239" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:29.559ex; height:3.009ex;" alt="{\displaystyle \Psi _{n\ell m}(r,\theta ,\phi )=R(r)\,\,Y_{\ell }^{m}\!(\theta ,\phi )}"></span> </p><p>Секоја од <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 _{n\ell m}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi mathvariant="normal">Ψ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mi>ℓ</mi> <mi>m</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Psi _{n\ell m}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d820fd99a0bfe9adf908e12079624bd241ab75f1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:5.155ex; height:2.509ex;" alt="{\displaystyle \Psi _{n\ell m}}"></span> компонентите на брановата функција сочинуваат една <a href="/wiki/%D0%90%D1%82%D0%BE%D0%BC%D1%81%D0%BA%D0%B0_%D0%BE%D1%80%D0%B1%D0%B8%D1%82%D0%B0%D0%BB%D0%B0" title="Атомска орбитала">атомска орбитала</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Поврзано"><span id=".D0.9F.D0.BE.D0.B2.D1.80.D0.B7.D0.B0.D0.BD.D0.BE"></span>Поврзано</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D0%91%D1%80%D0%B0%D0%BD%D0%BE%D0%B2%D0%B0_%D1%84%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D1%98%D0%B0&veaction=edit&section=9" title="Уреди го одделот „Поврзано“" class="mw-editsection-visualeditor"><span>уреди</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%D0%91%D1%80%D0%B0%D0%BD%D0%BE%D0%B2%D0%B0_%D1%84%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D1%98%D0%B0&action=edit&section=9" title="Уреди изворен код на одделот: Поврзано"><span>уреди извор</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/%D0%9A%D0%B2%D0%B0%D0%BD%D1%82%D0%BD%D0%B0_%D0%BC%D0%B5%D1%85%D0%B0%D0%BD%D0%B8%D0%BA%D0%B0" title="Квантна механика">Квантна механика</a></li> <li><a href="/wiki/%D0%92%D0%B5%D1%80%D0%BE%D1%98%D0%B0%D1%82%D0%BD%D0%BE%D1%81%D0%BD%D0%B0_%D1%80%D0%B0%D1%81%D0%BF%D1%80%D0%B5%D0%B4%D0%B5%D0%BB%D0%B1%D0%B0" title="Веројатносна распределба">Веројатносна распределба</a></li> <li><a href="/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">Шредингерова равенка</a></li> <li><a href="/wiki/%D0%9D%D0%B0%D1%87%D0%B5%D0%BB%D0%BE_%D0%BD%D0%B0_%D0%BD%D0%B5%D0%BE%D0%BF%D1%80%D0%B5%D0%B4%D0%B5%D0%BB%D0%B5%D0%BD%D0%BE%D1%81%D1%82" title="Начело на неопределеност">Хајзенберг несигурни односи</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Наводи"><span id=".D0.9D.D0.B0.D0.B2.D0.BE.D0.B4.D0.B8"></span>Наводи</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D0%91%D1%80%D0%B0%D0%BD%D0%BE%D0%B2%D0%B0_%D1%84%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D1%98%D0%B0&veaction=edit&section=10" title="Уреди го одделот „Наводи“" class="mw-editsection-visualeditor"><span>уреди</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%D0%91%D1%80%D0%B0%D0%BD%D0%BE%D0%B2%D0%B0_%D1%84%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D1%98%D0%B0&action=edit&section=10" title="Уреди изворен код на одделот: Наводи"><span>уреди извор</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="reflist" style="list-style-type: decimal;"> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-:0-1"><span class="mw-cite-backlink">↑ <sup><a href="#cite_ref-:0_1-0">1,0</a></sup> <sup><a href="#cite_ref-:0_1-1">1,1</a></sup></span> <span class="reference-text"><cite class="citation web"><a rel="nofollow" class="external text" href="https://arxiv.org/ftp/arxiv/papers/1001/1001.5085.pdf">„Значење таласне функције“</a> <span class="cs1-format">(PDF)</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=%D0%97%D0%BD%D0%B0%D1%87%D0%B5%D1%9A%D0%B5+%D1%82%D0%B0%D0%BB%D0%B0%D1%81%D0%BD%D0%B5+%D1%84%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D1%98%D0%B5&rft_id=https%3A%2F%2Farxiv.org%2Fftp%2Farxiv%2Fpapers%2F1001%2F1001.5085.pdf&rfr_id=info%3Asid%2Fmk.wikipedia.org%3A%D0%91%D1%80%D0%B0%D0%BD%D0%BE%D0%B2%D0%B0+%D1%84%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D1%98%D0%B0" class="Z3988"></span><style data-mw-deduplicate="TemplateStyles:r5289462">.mw-parser-output cite.citation{font-style:inherit}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .id-lock-free a,.mw-parser-output .citation .cs1-lock-free a{background-image:url("//upload.wikimedia.org/wikipedia/commons/thumb/6/65/Lock-green.svg/9px-Lock-green.svg.png");background-image:linear-gradient(transparent,transparent),url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg");background-repeat:no-repeat;background-size:9px;background-position:right .1em center}.mw-parser-output .id-lock-limited a,.mw-parser-output .id-lock-registration a,.mw-parser-output .citation .cs1-lock-limited a,.mw-parser-output .citation .cs1-lock-registration a{background-image:url("//upload.wikimedia.org/wikipedia/commons/thumb/d/d6/Lock-gray-alt-2.svg/9px-Lock-gray-alt-2.svg.png");background-image:linear-gradient(transparent,transparent),url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg");background-repeat:no-repeat;background-size:9px;background-position:right .1em center}.mw-parser-output .id-lock-subscription a,.mw-parser-output .citation .cs1-lock-subscription a{background-image:url("//upload.wikimedia.org/wikipedia/commons/thumb/a/aa/Lock-red-alt-2.svg/9px-Lock-red-alt-2.svg.png");background-image:linear-gradient(transparent,transparent),url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg");background-repeat:no-repeat;background-size:9px;background-position:right .1em center}.mw-parser-output .cs1-subscription,.mw-parser-output .cs1-registration{color:var(--color-subtle,#54595d)}.mw-parser-output .cs1-subscription span,.mw-parser-output .cs1-registration span{border-bottom:1px dotted;cursor:help}.mw-parser-output .cs1-ws-icon a{background-image:url("//upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Wikisource-logo.svg/12px-Wikisource-logo.svg.png");background-image:linear-gradient(transparent,transparent),url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg");background-repeat:no-repeat;background-size:12px;background-position:right .1em center}.mw-parser-output code.cs1-code{color:inherit;background:inherit;border:inherit;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;font-size:100%}.mw-parser-output .cs1-visible-error{font-size:100%}.mw-parser-output .cs1-maint{display:none;color:#33aa33;margin-left:0.3em}.mw-parser-output .cs1-subscription,.mw-parser-output .cs1-registration,.mw-parser-output .cs1-format{font-size:95%}.mw-parser-output .cs1-kern-left,.mw-parser-output .cs1-kern-wl-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right,.mw-parser-output .cs1-kern-wl-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}</style></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><a href="#cite_ref-2">↑</a></span> <span class="reference-text"><a href="#CITEREFBorn1927">Born 1927</a><span class="error harv-error" style="display: none; font-size:100%"> harvnb error: no target: CITEREFBorn1927 (<a href="/wiki/%D0%9A%D0%B0%D1%82%D0%B5%D0%B3%D0%BE%D1%80%D0%B8%D1%98%D0%B0:Harv_and_Sfn_template_errors" title="Категорија:Harv and Sfn template errors">help</a>)</span></span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><a href="#cite_ref-3">↑</a></span> <span class="reference-text"><a href="#CITEREFHeisenberg1958">Heisenberg 1958</a><span class="error harv-error" style="display: none; font-size:100%"> harvnb error: no target: CITEREFHeisenberg1958 (<a href="/wiki/%D0%9A%D0%B0%D1%82%D0%B5%D0%B3%D0%BE%D1%80%D0%B8%D1%98%D0%B0:Harv_and_Sfn_template_errors" title="Категорија:Harv and Sfn template errors">help</a>)</span></span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><a href="#cite_ref-4">↑</a></span> <span class="reference-text"><a href="/wiki/%D0%92%D0%B5%D1%80%D0%BD%D0%B5%D1%80_%D0%A5%D0%B0%D1%98%D0%B7%D0%B5%D0%BD%D0%B1%D0%B5%D1%80%D0%B3" title="Вернер Хајзенберг">Heisenberg, W.</a> (1927/1985/2009). Heisenberg is translated by <a href="#CITEREFCamilleri2009">Camilleri 2009</a><span class="error harv-error" style="display: none; font-size:100%"> harvnb error: no target: CITEREFCamilleri2009 (<a href="/wiki/%D0%9A%D0%B0%D1%82%D0%B5%D0%B3%D0%BE%D1%80%D0%B8%D1%98%D0%B0:Harv_and_Sfn_template_errors" title="Категорија:Harv and Sfn template errors">help</a>)</span>, (from <a href="#CITEREFBohr1985">Bohr 1985</a><span class="error harv-error" style="display: none; font-size:100%"> harvnb error: no target: CITEREFBohr1985 (<a href="/wiki/%D0%9A%D0%B0%D1%82%D0%B5%D0%B3%D0%BE%D1%80%D0%B8%D1%98%D0%B0:Harv_and_Sfn_template_errors" title="Категорија:Harv and Sfn template errors">help</a>)</span>).</span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><a href="#cite_ref-5">↑</a></span> <span class="reference-text"><a href="#CITEREFMurdoch1987">Murdoch 1987</a><span class="error harv-error" style="display: none; font-size:100%"> harvnb error: no target: CITEREFMurdoch1987 (<a href="/wiki/%D0%9A%D0%B0%D1%82%D0%B5%D0%B3%D0%BE%D1%80%D0%B8%D1%98%D0%B0:Harv_and_Sfn_template_errors" title="Категорија:Harv and Sfn template errors">help</a>)</span></span> </li> <li id="cite_note-6"><span class="mw-cite-backlink"><a href="#cite_ref-6">↑</a></span> <span class="reference-text"><a href="#CITEREFde_Broglie1960">de Broglie 1960</a><span class="error harv-error" style="display: none; font-size:100%"> harvnb error: no target: CITEREFde_Broglie1960 (<a href="/wiki/%D0%9A%D0%B0%D1%82%D0%B5%D0%B3%D0%BE%D1%80%D0%B8%D1%98%D0%B0:Harv_and_Sfn_template_errors" title="Категорија:Harv and Sfn template errors">help</a>)</span></span> </li> <li id="cite_note-7"><span class="mw-cite-backlink"><a href="#cite_ref-7">↑</a></span> <span class="reference-text"><a href="#CITEREFLandauLifshitz">Landau & Lifshitz</a><span class="error harv-error" style="display: none; font-size:100%"> harvnb error: no target: CITEREFLandauLifshitz (<a href="/wiki/%D0%9A%D0%B0%D1%82%D0%B5%D0%B3%D0%BE%D1%80%D0%B8%D1%98%D0%B0:Harv_and_Sfn_template_errors" title="Категорија:Harv and Sfn template errors">help</a>)</span></span> </li> <li id="cite_note-8"><span class="mw-cite-backlink"><a href="#cite_ref-8">↑</a></span> <span class="reference-text"><a href="#CITEREFNewton2002">Newton 2002</a><span class="error harv-error" style="display: none; font-size:100%"> harvnb error: no target: CITEREFNewton2002 (<a href="/wiki/%D0%9A%D0%B0%D1%82%D0%B5%D0%B3%D0%BE%D1%80%D0%B8%D1%98%D0%B0:Harv_and_Sfn_template_errors" title="Категорија:Harv and Sfn template errors">help</a>)</span></span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="Литература"><span id=".D0.9B.D0.B8.D1.82.D0.B5.D1.80.D0.B0.D1.82.D1.83.D1.80.D0.B0"></span>Литература</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D0%91%D1%80%D0%B0%D0%BD%D0%BE%D0%B2%D0%B0_%D1%84%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D1%98%D0%B0&veaction=edit&section=11" title="Уреди го одделот „Литература“" class="mw-editsection-visualeditor"><span>уреди</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%D0%91%D1%80%D0%B0%D0%BD%D0%BE%D0%B2%D0%B0_%D1%84%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D1%98%D0%B0&action=edit&section=11" title="Уреди изворен код на одделот: Литература"><span>уреди извор</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r3953304">.mw-parser-output .refbegin{font-size:90%;margin-bottom:0.5em}.mw-parser-output .refbegin-hanging-indents>ul{list-style-type:none;margin-left:0}.mw-parser-output .refbegin-hanging-indents>ul>li,.mw-parser-output .refbegin-hanging-indents>dl>dd{margin-left:0;padding-left:3.2em;text-indent:-3.2em;list-style:none}.mw-parser-output .refbegin-100{font-size:100%}</style><div class="refbegin reflist columns references-column-width" style="-moz-column-width: 30em; -webkit-column-width: 30em; column-width: 30em;"> <ul><li><cite id="CITEREFAtkins1974" class="citation book">Atkins, P. W. (1974). <i>Quanta: A Handbook of Concepts</i>. <a href="/wiki/ISBN" title="ISBN">ISBN</a> <a href="/wiki/%D0%A1%D0%BF%D0%B5%D1%86%D0%B8%D1%98%D0%B0%D0%BB%D0%BD%D0%B0:%D0%9F%D0%B5%D1%87%D0%B0%D1%82%D0%B5%D0%BD%D0%98%D0%B7%D0%B2%D0%BE%D1%80/978-0-19-855494-3" title="Специјална:ПечатенИзвор/978-0-19-855494-3"><bdi>978-0-19-855494-3</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Quanta%3A+A+Handbook+of+Concepts&rft.date=1974&rft.isbn=978-0-19-855494-3&rft.aulast=Atkins&rft.aufirst=P.+W.&rfr_id=info%3Asid%2Fmk.wikipedia.org%3A%D0%91%D1%80%D0%B0%D0%BD%D0%BE%D0%B2%D0%B0+%D1%84%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D1%98%D0%B0" class="Z3988"></span><span class="cs1-maint citation-comment">CS1-одржување: ref=harv (<a href="/wiki/%D0%9A%D0%B0%D1%82%D0%B5%D0%B3%D0%BE%D1%80%D0%B8%D1%98%D0%B0:CS1-%D0%BE%D0%B4%D1%80%D0%B6%D1%83%D0%B2%D0%B0%D1%9A%D0%B5:_ref%3Dharv" title="Категорија:CS1-одржување: ref=harv">link</a>)</span><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r5289462"></li> <li><cite id="CITEREFAronsPeppard1965" class="citation journal">Arons, A. B.; Peppard, M. B. (1965). <a rel="nofollow" class="external text" href="https://web.archive.org/web/20160304031335/http://astro1.panet.utoledo.edu/~ljc/PE_eng.pdf">„Einstein's proposal of the photon concept: A translation of the <i>Annalen der Physik</i> paper of 1905“</a> <span class="cs1-format">(PDF)</span>. <i><a href="/w/index.php?title=American_Journal_of_Physics&action=edit&redlink=1" class="new" title="American Journal of Physics (страницата не постои)">American Journal of Physics</a></i>. <b>33</b> (5): 367. <a href="/wiki/Bibcode" title="Bibcode">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1965AmJPh..33..367A">1965AmJPh..33..367A</a>. <a href="/wiki/Doi" class="mw-redirect" title="Doi">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1119%2F1.1971542">10.1119/1.1971542</a>. Архивирано од <a rel="nofollow" class="external text" href="http://astro1.panet.utoledo.edu/~ljc/PE_eng.pdf">изворникот</a> <span class="cs1-format">(PDF)</span> на 4 март 2016<span class="reference-accessdate">. Посетено на 26 јуни 2019</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=American+Journal+of+Physics&rft.atitle=Einstein%27s+proposal+of+the+photon+concept%3A+A+translation+of+the+Annalen+der+Physik+paper+of+1905&rft.volume=33&rft.issue=5&rft.pages=367&rft.date=1965&rft_id=info%3Adoi%2F10.1119%2F1.1971542&rft_id=info%3Abibcode%2F1965AmJPh..33..367A&rft.aulast=Arons&rft.aufirst=A.+B.&rft.au=Peppard%2C+M.+B.&rft_id=http%3A%2F%2Fastro1.panet.utoledo.edu%2F~ljc%2FPE_eng.pdf&rfr_id=info%3Asid%2Fmk.wikipedia.org%3A%D0%91%D1%80%D0%B0%D0%BD%D0%BE%D0%B2%D0%B0+%D1%84%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D1%98%D0%B0" class="Z3988"></span><span class="cs1-maint citation-comment">CS1-одржување: ref=harv (<a href="/wiki/%D0%9A%D0%B0%D1%82%D0%B5%D0%B3%D0%BE%D1%80%D0%B8%D1%98%D0%B0:CS1-%D0%BE%D0%B4%D1%80%D0%B6%D1%83%D0%B2%D0%B0%D1%9A%D0%B5:_ref%3Dharv" title="Категорија:CS1-одржување: ref=harv">link</a>)</span><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r5289462"></li> <li><cite id="CITEREFBohr1985" class="citation book"><a href="/w/index.php?title=Niels_Bohr&action=edit&redlink=1" class="new" title="Niels Bohr (страницата не постои)">Bohr, N.</a> (1985). J. Kalckar (уред.). <i>Niels Bohr - Collected Works: Foundations of Quantum Physics I (1926 - 1932)</i>. <b>6</b>. Amsterdam: North Holland. <a href="/wiki/ISBN" title="ISBN">ISBN</a> <a href="/wiki/%D0%A1%D0%BF%D0%B5%D1%86%D0%B8%D1%98%D0%B0%D0%BB%D0%BD%D0%B0:%D0%9F%D0%B5%D1%87%D0%B0%D1%82%D0%B5%D0%BD%D0%98%D0%B7%D0%B2%D0%BE%D1%80/9780444532893" title="Специјална:ПечатенИзвор/9780444532893"><bdi>9780444532893</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Niels+Bohr+-+Collected+Works%3A+Foundations+of+Quantum+Physics+I+%281926+-+1932%29&rft.place=Amsterdam&rft.pub=North+Holland&rft.date=1985&rft.isbn=9780444532893&rft.aulast=Bohr&rft.aufirst=N.&rfr_id=info%3Asid%2Fmk.wikipedia.org%3A%D0%91%D1%80%D0%B0%D0%BD%D0%BE%D0%B2%D0%B0+%D1%84%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D1%98%D0%B0" class="Z3988"></span><span class="cs1-maint citation-comment">CS1-одржување: ref=harv (<a href="/wiki/%D0%9A%D0%B0%D1%82%D0%B5%D0%B3%D0%BE%D1%80%D0%B8%D1%98%D0%B0:CS1-%D0%BE%D0%B4%D1%80%D0%B6%D1%83%D0%B2%D0%B0%D1%9A%D0%B5:_ref%3Dharv" title="Категорија:CS1-одржување: ref=harv">link</a>)</span><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r5289462"></li> <li><cite id="CITEREFBorn1926a" class="citation journal">Born, M. (1926a). „Zur Quantenmechanik der Stoßvorgange“. <i>Z. Phys</i>. <b>37</b> (12): 863–867. <a href="/wiki/Bibcode" title="Bibcode">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1926ZPhy...37..863B">1926ZPhy...37..863B</a>. <a href="/wiki/Doi" class="mw-redirect" title="Doi">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2Fbf01397477">10.1007/bf01397477</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Z.+Phys.&rft.atitle=Zur+Quantenmechanik+der+Sto%C3%9Fvorgange&rft.volume=37&rft.issue=12&rft.pages=863-867&rft.date=1926&rft_id=info%3Adoi%2F10.1007%2Fbf01397477&rft_id=info%3Abibcode%2F1926ZPhy...37..863B&rft.aulast=Born&rft.aufirst=M.&rfr_id=info%3Asid%2Fmk.wikipedia.org%3A%D0%91%D1%80%D0%B0%D0%BD%D0%BE%D0%B2%D0%B0+%D1%84%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D1%98%D0%B0" class="Z3988"></span><span class="cs1-maint citation-comment">CS1-одржување: ref=harv (<a href="/wiki/%D0%9A%D0%B0%D1%82%D0%B5%D0%B3%D0%BE%D1%80%D0%B8%D1%98%D0%B0:CS1-%D0%BE%D0%B4%D1%80%D0%B6%D1%83%D0%B2%D0%B0%D1%9A%D0%B5:_ref%3Dharv" title="Категорија:CS1-одржување: ref=harv">link</a>)</span><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r5289462"></li> <li><cite id="CITEREFBorn1926b" class="citation journal">Born, M. (1926b). „Quantenmechanik der Stoßvorgange“. <i>Z. Phys</i>. <b>38</b> (11–12): 803–827. <a href="/wiki/Bibcode" title="Bibcode">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1926ZPhy...38..803B">1926ZPhy...38..803B</a>. <a href="/wiki/Doi" class="mw-redirect" title="Doi">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2Fbf01397184">10.1007/bf01397184</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Z.+Phys.&rft.atitle=Quantenmechanik+der+Sto%C3%9Fvorgange&rft.volume=38&rft.issue=11%E2%80%9312&rft.pages=803-827&rft.date=1926&rft_id=info%3Adoi%2F10.1007%2Fbf01397184&rft_id=info%3Abibcode%2F1926ZPhy...38..803B&rft.aulast=Born&rft.aufirst=M.&rfr_id=info%3Asid%2Fmk.wikipedia.org%3A%D0%91%D1%80%D0%B0%D0%BD%D0%BE%D0%B2%D0%B0+%D1%84%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D1%98%D0%B0" class="Z3988"></span><span class="cs1-maint citation-comment">CS1-одржување: ref=harv (<a href="/wiki/%D0%9A%D0%B0%D1%82%D0%B5%D0%B3%D0%BE%D1%80%D0%B8%D1%98%D0%B0:CS1-%D0%BE%D0%B4%D1%80%D0%B6%D1%83%D0%B2%D0%B0%D1%9A%D0%B5:_ref%3Dharv" title="Категорија:CS1-одржување: ref=harv">link</a>)</span><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r5289462"></li> <li><cite id="CITEREFBorn1927" class="citation journal"><a href="/w/index.php?title=Max_Born&action=edit&redlink=1" class="new" title="Max Born (страницата не постои)">Born, M.</a> (1927). „Physical aspects of quantum mechanics“. <i>Nature</i>. <b>119</b> (2992): 354–357. <a href="/wiki/Bibcode" title="Bibcode">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1927Natur.119..354B">1927Natur.119..354B</a>. <a href="/wiki/Doi" class="mw-redirect" title="Doi">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1038%2F119354a0">10.1038/119354a0</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Nature&rft.atitle=Physical+aspects+of+quantum+mechanics&rft.volume=119&rft.issue=2992&rft.pages=354-357&rft.date=1927&rft_id=info%3Adoi%2F10.1038%2F119354a0&rft_id=info%3Abibcode%2F1927Natur.119..354B&rft.aulast=Born&rft.aufirst=M.&rfr_id=info%3Asid%2Fmk.wikipedia.org%3A%D0%91%D1%80%D0%B0%D0%BD%D0%BE%D0%B2%D0%B0+%D1%84%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D1%98%D0%B0" class="Z3988"></span><span class="cs1-maint citation-comment">CS1-одржување: ref=harv (<a href="/wiki/%D0%9A%D0%B0%D1%82%D0%B5%D0%B3%D0%BE%D1%80%D0%B8%D1%98%D0%B0:CS1-%D0%BE%D0%B4%D1%80%D0%B6%D1%83%D0%B2%D0%B0%D1%9A%D0%B5:_ref%3Dharv" title="Категорија:CS1-одржување: ref=harv">link</a>)</span><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r5289462"></li> <li><a href="/w/index.php?title=Max_Born&action=edit&redlink=1" class="new" title="Max Born (страницата не постои)">Born, M.</a> (1954). <cite class="citation web"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20121019194414/http://www.nobelprize.org/nobel_prizes/physics/laureates/1954/born-lecture.pdf">„The statistical interpretation of quantum mechanics“</a> <span class="cs1-format">(PDF)</span>. <i>Nobel Lecture</i>. 11 декември 1954. Архивирано од <a rel="nofollow" class="external text" href="http://nobelprize.org/nobel_prizes/physics/laureates/1954/born-lecture.pdf">изворникот</a> <span class="cs1-format">(PDF)</span> на 19 октомври 2012<span class="reference-accessdate">. Посетено на 26 јуни 2019</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Nobel+Lecture&rft.atitle=The+statistical+interpretation+of+quantum+mechanics&rft.date=1954-12-11&rft_id=http%3A%2F%2Fnobelprize.org%2Fnobel_prizes%2Fphysics%2Flaureates%2F1954%2Fborn-lecture.pdf&rfr_id=info%3Asid%2Fmk.wikipedia.org%3A%D0%91%D1%80%D0%B0%D0%BD%D0%BE%D0%B2%D0%B0+%D1%84%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D1%98%D0%B0" class="Z3988"></span><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r5289462"></li> <li><cite id="CITEREFde_Broglie1923" class="citation journal">de Broglie, L. (1923). „Radiations—Ondes et quanta“ [Radiation—Waves and quanta]. <i>Comptes Rendus</i> (француски). <b>177</b>: 507–510, 548, 630.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Comptes+Rendus&rft.atitle=Radiations%E2%80%94Ondes+et+quanta&rft.volume=177&rft.pages=507-510%2C+548%2C+630&rft.date=1923&rft.aulast=de+Broglie&rft.aufirst=L.&rfr_id=info%3Asid%2Fmk.wikipedia.org%3A%D0%91%D1%80%D0%B0%D0%BD%D0%BE%D0%B2%D0%B0+%D1%84%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D1%98%D0%B0" class="Z3988"></span><span class="cs1-maint citation-comment">CS1-одржување: ref=harv (<a href="/wiki/%D0%9A%D0%B0%D1%82%D0%B5%D0%B3%D0%BE%D1%80%D0%B8%D1%98%D0%B0:CS1-%D0%BE%D0%B4%D1%80%D0%B6%D1%83%D0%B2%D0%B0%D1%9A%D0%B5:_ref%3Dharv" title="Категорија:CS1-одржување: ref=harv">link</a>)</span><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r5289462"> <a rel="nofollow" class="external text" href="http://www.academie-sciences.fr/pdf/dossiers/Broglie/Broglie_pdf/CR1923_p507.pdf">Online copy (French)</a> <a rel="nofollow" class="external text" href="http://www.davis-inc.com/physics/broglie/broglie.shtml">Online copy (English)</a></li> <li><cite id="CITEREFde_Broglie1960" class="citation book"><a href="/w/index.php?title=Louis_de_Broglie&action=edit&redlink=1" class="new" title="Louis de Broglie (страницата не постои)">de Broglie, L.</a> (1960). <i>Non-linear Wave Mechanics: a Causal Interpretation</i>. Amsterdam: Elsevier.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Non-linear+Wave+Mechanics%3A+a+Causal+Interpretation&rft.place=Amsterdam&rft.pub=Elsevier&rft.date=1960&rft.aulast=de+Broglie&rft.aufirst=L.&rfr_id=info%3Asid%2Fmk.wikipedia.org%3A%D0%91%D1%80%D0%B0%D0%BD%D0%BE%D0%B2%D0%B0+%D1%84%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D1%98%D0%B0" class="Z3988"></span><span class="cs1-maint citation-comment">CS1-одржување: ref=harv (<a href="/wiki/%D0%9A%D0%B0%D1%82%D0%B5%D0%B3%D0%BE%D1%80%D0%B8%D1%98%D0%B0:CS1-%D0%BE%D0%B4%D1%80%D0%B6%D1%83%D0%B2%D0%B0%D1%9A%D0%B5:_ref%3Dharv" title="Категорија:CS1-одржување: ref=harv">link</a>)</span><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r5289462"></li> <li><cite id="CITEREFCamilleri2009" class="citation book">Camilleri, K. (2009). <i>Heisenberg and the Interpretation of Quantum Mechanics: the Physicist as Philosopher</i>. Cambridge UK: Cambridge University Press. <a href="/wiki/ISBN" title="ISBN">ISBN</a> <a href="/wiki/%D0%A1%D0%BF%D0%B5%D1%86%D0%B8%D1%98%D0%B0%D0%BB%D0%BD%D0%B0:%D0%9F%D0%B5%D1%87%D0%B0%D1%82%D0%B5%D0%BD%D0%98%D0%B7%D0%B2%D0%BE%D1%80/978-0-521-88484-6" title="Специјална:ПечатенИзвор/978-0-521-88484-6"><bdi>978-0-521-88484-6</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Heisenberg+and+the+Interpretation+of+Quantum+Mechanics%3A+the+Physicist+as+Philosopher&rft.place=Cambridge+UK&rft.pub=Cambridge+University+Press&rft.date=2009&rft.isbn=978-0-521-88484-6&rft.aulast=Camilleri&rft.aufirst=K.&rfr_id=info%3Asid%2Fmk.wikipedia.org%3A%D0%91%D1%80%D0%B0%D0%BD%D0%BE%D0%B2%D0%B0+%D1%84%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D1%98%D0%B0" class="Z3988"></span><span class="cs1-maint citation-comment">CS1-одржување: ref=harv (<a href="/wiki/%D0%9A%D0%B0%D1%82%D0%B5%D0%B3%D0%BE%D1%80%D0%B8%D1%98%D0%B0:CS1-%D0%BE%D0%B4%D1%80%D0%B6%D1%83%D0%B2%D0%B0%D1%9A%D0%B5:_ref%3Dharv" title="Категорија:CS1-одржување: ref=harv">link</a>)</span><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r5289462"></li> <li><cite id="CITEREFByronFuller1992" class="citation book">Byron, F. W.; <a href="/w/index.php?title=Robert_W._Fuller&action=edit&redlink=1" class="new" title="Robert W. Fuller (страницата не постои)">Fuller, R. W.</a> (1992) [1969]. <i>Mathematics of Classical and Quantum Physics</i>. Dover Books on Physics (revised. изд.). <a href="/w/index.php?title=Dover_Publications&action=edit&redlink=1" class="new" title="Dover Publications (страницата не постои)">Dover Publications</a>. <a href="/wiki/ISBN" title="ISBN">ISBN</a> <a href="/wiki/%D0%A1%D0%BF%D0%B5%D1%86%D0%B8%D1%98%D0%B0%D0%BB%D0%BD%D0%B0:%D0%9F%D0%B5%D1%87%D0%B0%D1%82%D0%B5%D0%BD%D0%98%D0%B7%D0%B2%D0%BE%D1%80/978-0-486-67164-2" title="Специјална:ПечатенИзвор/978-0-486-67164-2"><bdi>978-0-486-67164-2</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Mathematics+of+Classical+and+Quantum+Physics&rft.series=Dover+Books+on+Physics&rft.edition=revised&rft.pub=Dover+Publications&rft.date=1992&rft.isbn=978-0-486-67164-2&rft.aulast=Byron&rft.aufirst=F.+W.&rft.au=Fuller%2C+R.+W.&rfr_id=info%3Asid%2Fmk.wikipedia.org%3A%D0%91%D1%80%D0%B0%D0%BD%D0%BE%D0%B2%D0%B0+%D1%84%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D1%98%D0%B0" class="Z3988"></span><span class="cs1-maint citation-comment">CS1-одржување: ref=harv (<a href="/wiki/%D0%9A%D0%B0%D1%82%D0%B5%D0%B3%D0%BE%D1%80%D0%B8%D1%98%D0%B0:CS1-%D0%BE%D0%B4%D1%80%D0%B6%D1%83%D0%B2%D0%B0%D1%9A%D0%B5:_ref%3Dharv" title="Категорија:CS1-одржување: ref=harv">link</a>)</span><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r5289462"></li> <li><cite id="CITEREFConway1990" class="citation book"><a href="/w/index.php?title=John_B._Conway&action=edit&redlink=1" class="new" title="John B. Conway (страницата не постои)">Conway, J. B.</a> (1990). <i>A Course in Functional Analysis</i>. Graduate Texts in Mathematics. <b>96</b>. <a href="/w/index.php?title=Springer_Verlag&action=edit&redlink=1" class="new" title="Springer Verlag (страницата не постои)">Springer Verlag</a>. <a href="/wiki/ISBN" title="ISBN">ISBN</a> <a href="/wiki/%D0%A1%D0%BF%D0%B5%D1%86%D0%B8%D1%98%D0%B0%D0%BB%D0%BD%D0%B0:%D0%9F%D0%B5%D1%87%D0%B0%D1%82%D0%B5%D0%BD%D0%98%D0%B7%D0%B2%D0%BE%D1%80/978-0-387-97245-9" title="Специјална:ПечатенИзвор/978-0-387-97245-9"><bdi>978-0-387-97245-9</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=A+Course+in+Functional+Analysis&rft.series=Graduate+Texts+in+Mathematics&rft.pub=Springer+Verlag&rft.date=1990&rft.isbn=978-0-387-97245-9&rft.aulast=Conway&rft.aufirst=J.+B.&rfr_id=info%3Asid%2Fmk.wikipedia.org%3A%D0%91%D1%80%D0%B0%D0%BD%D0%BE%D0%B2%D0%B0+%D1%84%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D1%98%D0%B0" class="Z3988"></span><span class="cs1-maint citation-comment">CS1-одржување: ref=harv (<a href="/wiki/%D0%9A%D0%B0%D1%82%D0%B5%D0%B3%D0%BE%D1%80%D0%B8%D1%98%D0%B0:CS1-%D0%BE%D0%B4%D1%80%D0%B6%D1%83%D0%B2%D0%B0%D1%9A%D0%B5:_ref%3Dharv" title="Категорија:CS1-одржување: ref=harv">link</a>)</span><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r5289462"></li> <li><cite id="CITEREFDirac1982" class="citation book"><a href="/w/index.php?title=Paul_Dirac&action=edit&redlink=1" class="new" title="Paul Dirac (страницата не постои)">Dirac, P. A. M.</a> (1982). <i>The principles of quantum mechanics</i>. The international series on monographs on physics (4. изд.). Oxford University Press. <a href="/wiki/ISBN" title="ISBN">ISBN</a> <a href="/wiki/%D0%A1%D0%BF%D0%B5%D1%86%D0%B8%D1%98%D0%B0%D0%BB%D0%BD%D0%B0:%D0%9F%D0%B5%D1%87%D0%B0%D1%82%D0%B5%D0%BD%D0%98%D0%B7%D0%B2%D0%BE%D1%80/0_19_852011_5" title="Специјална:ПечатенИзвор/0 19 852011 5"><bdi>0 19 852011 5</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+principles+of+quantum+mechanics&rft.series=The+international+series+on+monographs+on+physics&rft.edition=4&rft.pub=Oxford+University+Press&rft.date=1982&rft.isbn=0198520115&rft.aulast=Dirac&rft.aufirst=P.+A.+M.&rfr_id=info%3Asid%2Fmk.wikipedia.org%3A%D0%91%D1%80%D0%B0%D0%BD%D0%BE%D0%B2%D0%B0+%D1%84%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D1%98%D0%B0" class="Z3988"></span><span class="cs1-maint citation-comment">CS1-одржување: ref=harv (<a href="/wiki/%D0%9A%D0%B0%D1%82%D0%B5%D0%B3%D0%BE%D1%80%D0%B8%D1%98%D0%B0:CS1-%D0%BE%D0%B4%D1%80%D0%B6%D1%83%D0%B2%D0%B0%D1%9A%D0%B5:_ref%3Dharv" title="Категорија:CS1-одржување: ref=harv">link</a>)</span><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r5289462"></li> <li><cite id="CITEREFDirac1939" class="citation journal">Dirac, P. A. M. (1939). <a rel="nofollow" class="external text" href="https://web.archive.org/web/20131203033616/http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=2031476">„A new notation for quantum mechanics“</a>. <i>Mathematical Proceedings of the Cambridge Philosophical Society</i>. <b>35</b> (3): 416–418. <a href="/wiki/Bibcode" title="Bibcode">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1939PCPS...35..416D">1939PCPS...35..416D</a>. <a href="/wiki/Doi" class="mw-redirect" title="Doi">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1017%2FS0305004100021162">10.1017/S0305004100021162</a>. Архивирано од <a rel="nofollow" class="external text" href="http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=2031476">изворникот</a> на 2013-12-03<span class="reference-accessdate">. Посетено на <span class="nowrap">2021-12-01</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Mathematical+Proceedings+of+the+Cambridge+Philosophical+Society&rft.atitle=A+new+notation+for+quantum+mechanics&rft.volume=35&rft.issue=3&rft.pages=416-418&rft.date=1939&rft_id=info%3Adoi%2F10.1017%2FS0305004100021162&rft_id=info%3Abibcode%2F1939PCPS...35..416D&rft.aulast=Dirac&rft.aufirst=P.+A.+M.&rft_id=http%3A%2F%2Fjournals.cambridge.org%2Faction%2FdisplayAbstract%3FfromPage%3Donline%26aid%3D2031476&rfr_id=info%3Asid%2Fmk.wikipedia.org%3A%D0%91%D1%80%D0%B0%D0%BD%D0%BE%D0%B2%D0%B0+%D1%84%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D1%98%D0%B0" class="Z3988"></span><span class="cs1-maint citation-comment">CS1-одржување: ref=harv (<a href="/wiki/%D0%9A%D0%B0%D1%82%D0%B5%D0%B3%D0%BE%D1%80%D0%B8%D1%98%D0%B0:CS1-%D0%BE%D0%B4%D1%80%D0%B6%D1%83%D0%B2%D0%B0%D1%9A%D0%B5:_ref%3Dharv" title="Категорија:CS1-одржување: ref=harv">link</a>)</span><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r5289462"></li> <li><cite id="CITEREFEinstein1905" class="citation journal"><a href="/wiki/Albert_Einstein" class="mw-redirect" title="Albert Einstein">Einstein, A.</a> (1905). „Über einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt“. <i><a href="/w/index.php?title=Annalen_der_Physik&action=edit&redlink=1" class="new" title="Annalen der Physik (страницата не постои)">Annalen der Physik</a></i> (германски). <b>17</b> (6): 132–148. <a href="/wiki/Bibcode" title="Bibcode">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1905AnP...322..132E">1905AnP...322..132E</a>. <a href="/wiki/Doi" class="mw-redirect" title="Doi">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1002%2Fandp.19053220607">10.1002/andp.19053220607</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Annalen+der+Physik&rft.atitle=%C3%9Cber+einen+die+Erzeugung+und+Verwandlung+des+Lichtes+betreffenden+heuristischen+Gesichtspunkt&rft.volume=17&rft.issue=6&rft.pages=132-148&rft.date=1905&rft_id=info%3Adoi%2F10.1002%2Fandp.19053220607&rft_id=info%3Abibcode%2F1905AnP...322..132E&rft.aulast=Einstein&rft.aufirst=A.&rfr_id=info%3Asid%2Fmk.wikipedia.org%3A%D0%91%D1%80%D0%B0%D0%BD%D0%BE%D0%B2%D0%B0+%D1%84%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D1%98%D0%B0" class="Z3988"></span><span class="cs1-maint citation-comment">CS1-одржување: ref=harv (<a href="/wiki/%D0%9A%D0%B0%D1%82%D0%B5%D0%B3%D0%BE%D1%80%D0%B8%D1%98%D0%B0:CS1-%D0%BE%D0%B4%D1%80%D0%B6%D1%83%D0%B2%D0%B0%D1%9A%D0%B5:_ref%3Dharv" title="Категорија:CS1-одржување: ref=harv">link</a>)</span><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r5289462"></li> <li><cite id="CITEREFEinstein1916" class="citation journal">Einstein, A. (1916). „Zur Quantentheorie der Strahlung“. <i>Mitteilungen der Physikalischen Gesellschaft Zürich</i>. <b>18</b>: 47–62.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Mitteilungen+der+Physikalischen+Gesellschaft+Z%C3%BCrich&rft.atitle=Zur+Quantentheorie+der+Strahlung&rft.volume=18&rft.pages=47-62&rft.date=1916&rft.aulast=Einstein&rft.aufirst=A.&rfr_id=info%3Asid%2Fmk.wikipedia.org%3A%D0%91%D1%80%D0%B0%D0%BD%D0%BE%D0%B2%D0%B0+%D1%84%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D1%98%D0%B0" class="Z3988"></span><span class="cs1-maint citation-comment">CS1-одржување: ref=harv (<a href="/wiki/%D0%9A%D0%B0%D1%82%D0%B5%D0%B3%D0%BE%D1%80%D0%B8%D1%98%D0%B0:CS1-%D0%BE%D0%B4%D1%80%D0%B6%D1%83%D0%B2%D0%B0%D1%9A%D0%B5:_ref%3Dharv" title="Категорија:CS1-одржување: ref=harv">link</a>)</span><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r5289462"></li> <li><cite id="CITEREFEinstein1917" class="citation journal">Einstein, A. (1917). „Zur Quantentheorie der Strahlung“. <i><a href="/w/index.php?title=Physikalische_Zeitschrift&action=edit&redlink=1" class="new" title="Physikalische Zeitschrift (страницата не постои)">Physikalische Zeitschrift</a></i> (германски). <b>18</b>: 121–128. <a href="/wiki/Bibcode" title="Bibcode">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1917PhyZ...18..121E">1917PhyZ...18..121E</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physikalische+Zeitschrift&rft.atitle=Zur+Quantentheorie+der+Strahlung&rft.volume=18&rft.pages=121-128&rft.date=1917&rft_id=info%3Abibcode%2F1917PhyZ...18..121E&rft.aulast=Einstein&rft.aufirst=A.&rfr_id=info%3Asid%2Fmk.wikipedia.org%3A%D0%91%D1%80%D0%B0%D0%BD%D0%BE%D0%B2%D0%B0+%D1%84%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D1%98%D0%B0" class="Z3988"></span><span class="cs1-maint citation-comment">CS1-одржување: ref=harv (<a href="/wiki/%D0%9A%D0%B0%D1%82%D0%B5%D0%B3%D0%BE%D1%80%D0%B8%D1%98%D0%B0:CS1-%D0%BE%D0%B4%D1%80%D0%B6%D1%83%D0%B2%D0%B0%D1%9A%D0%B5:_ref%3Dharv" title="Категорија:CS1-одржување: ref=harv">link</a>)</span><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r5289462"></li> <li><cite id="CITEREFEinstein1998" class="citation book">Einstein, A. (1998). P. A. Schlipp (уред.). <i>Albert Einstein: Philosopher-Scientist</i>. The Library of Living Philosophers. <b>VII</b> (3. изд.). La Salle Publishing Company, Illinois: Open Court. <a href="/wiki/ISBN" title="ISBN">ISBN</a> <a href="/wiki/%D0%A1%D0%BF%D0%B5%D1%86%D0%B8%D1%98%D0%B0%D0%BB%D0%BD%D0%B0:%D0%9F%D0%B5%D1%87%D0%B0%D1%82%D0%B5%D0%BD%D0%98%D0%B7%D0%B2%D0%BE%D1%80/978-0-87548-133-3" title="Специјална:ПечатенИзвор/978-0-87548-133-3"><bdi>978-0-87548-133-3</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Albert+Einstein%3A+Philosopher-Scientist&rft.place=La+Salle+Publishing+Company%2C+Illinois&rft.series=The+Library+of+Living+Philosophers&rft.edition=3&rft.pub=Open+Court&rft.date=1998&rft.isbn=978-0-87548-133-3&rft.aulast=Einstein&rft.aufirst=A.&rfr_id=info%3Asid%2Fmk.wikipedia.org%3A%D0%91%D1%80%D0%B0%D0%BD%D0%BE%D0%B2%D0%B0+%D1%84%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D1%98%D0%B0" class="Z3988"></span><span class="cs1-maint citation-comment">CS1-одржување: ref=harv (<a href="/wiki/%D0%9A%D0%B0%D1%82%D0%B5%D0%B3%D0%BE%D1%80%D0%B8%D1%98%D0%B0:CS1-%D0%BE%D0%B4%D1%80%D0%B6%D1%83%D0%B2%D0%B0%D1%9A%D0%B5:_ref%3Dharv" title="Категорија:CS1-одржување: ref=harv">link</a>)</span><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r5289462"></li> <li><cite id="CITEREFEisbergResnick1985" class="citation book">Eisberg, R.; Resnick, R. (1985). <i>Quantum Physics of Atoms, Molecules, Solids, Nuclei and Particles</i> (2. изд.). John Wiley & Sons. <a href="/wiki/ISBN" title="ISBN">ISBN</a> <a href="/wiki/%D0%A1%D0%BF%D0%B5%D1%86%D0%B8%D1%98%D0%B0%D0%BB%D0%BD%D0%B0:%D0%9F%D0%B5%D1%87%D0%B0%D1%82%D0%B5%D0%BD%D0%98%D0%B7%D0%B2%D0%BE%D1%80/978-0-471-87373-0" title="Специјална:ПечатенИзвор/978-0-471-87373-0"><bdi>978-0-471-87373-0</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Quantum+Physics+of+Atoms%2C+Molecules%2C+Solids%2C+Nuclei+and+Particles&rft.edition=2&rft.pub=John+Wiley+%26+Sons&rft.date=1985&rft.isbn=978-0-471-87373-0&rft.aulast=Eisberg&rft.aufirst=R.&rft.au=Resnick%2C+R.&rfr_id=info%3Asid%2Fmk.wikipedia.org%3A%D0%91%D1%80%D0%B0%D0%BD%D0%BE%D0%B2%D0%B0+%D1%84%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D1%98%D0%B0" class="Z3988"></span><span class="cs1-maint citation-comment">CS1-одржување: ref=harv (<a href="/wiki/%D0%9A%D0%B0%D1%82%D0%B5%D0%B3%D0%BE%D1%80%D0%B8%D1%98%D0%B0:CS1-%D0%BE%D0%B4%D1%80%D0%B6%D1%83%D0%B2%D0%B0%D1%9A%D0%B5:_ref%3Dharv" title="Категорија:CS1-одржување: ref=harv">link</a>)</span><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r5289462"></li> <li><a href="/w/index.php?title=%D0%9F%D1%80%D0%B5%D0%B4%D0%BB%D0%BE%D1%88%D0%BA%D0%B0:%D0%9D%D0%B0%D0%B2%D0%B5%D0%B4%D0%B5%D0%BD%D0%B0_%D0%BA%D0%BD%D0%B8%D0%B3%D0%B0k&action=edit&redlink=1" class="new" title="Предлошка:Наведена книгаk (страницата не постои)">Предлошка:Наведена книгаk</a></li> <li><cite id="CITEREFGriffiths2004" class="citation book">Griffiths, D. J. (2004). <i>Introduction to Quantum Mechanics</i> (2. изд.). Essex England: Pearson Education Ltd. <a href="/wiki/ISBN" title="ISBN">ISBN</a> <a href="/wiki/%D0%A1%D0%BF%D0%B5%D1%86%D0%B8%D1%98%D0%B0%D0%BB%D0%BD%D0%B0:%D0%9F%D0%B5%D1%87%D0%B0%D1%82%D0%B5%D0%BD%D0%98%D0%B7%D0%B2%D0%BE%D1%80/978-0131118928" title="Специјална:ПечатенИзвор/978-0131118928"><bdi>978-0131118928</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Introduction+to+Quantum+Mechanics&rft.place=Essex+England&rft.edition=2&rft.pub=Pearson+Education+Ltd&rft.date=2004&rft.isbn=978-0131118928&rft.aulast=Griffiths&rft.aufirst=D.+J.&rfr_id=info%3Asid%2Fmk.wikipedia.org%3A%D0%91%D1%80%D0%B0%D0%BD%D0%BE%D0%B2%D0%B0+%D1%84%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D1%98%D0%B0" class="Z3988"></span><span class="cs1-maint citation-comment">CS1-одржување: ref=harv (<a href="/wiki/%D0%9A%D0%B0%D1%82%D0%B5%D0%B3%D0%BE%D1%80%D0%B8%D1%98%D0%B0:CS1-%D0%BE%D0%B4%D1%80%D0%B6%D1%83%D0%B2%D0%B0%D1%9A%D0%B5:_ref%3Dharv" title="Категорија:CS1-одржување: ref=harv">link</a>)</span><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r5289462"></li> <li><cite id="CITEREFHeisenberg1958" class="citation book"><a href="/w/index.php?title=Werner_Heisenberg&action=edit&redlink=1" class="new" title="Werner Heisenberg (страницата не постои)">Heisenberg, W.</a> (1958). <a rel="nofollow" class="external text" href="https://archive.org/details/physicsphilosoph0000heis"><i>Physics and Philosophy: the Revolution in Modern Science</i></a>. 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(1977), „Erwin Schrodinger's Reaction to Louis de Broglie's Thesis on the Quantum Theory.“, <i>Isis</i>, <b>68</b> (4): 606–609, <a href="/wiki/Doi" class="mw-redirect" title="Doi">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1086%2F351880">10.1086/351880</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Isis&rft.atitle=Erwin+Schrodinger%27s+Reaction+to+Louis+de+Broglie%27s+Thesis+on+the+Quantum+Theory.&rft.volume=68&rft.issue=4&rft.pages=606-609&rft.date=1977&rft_id=info%3Adoi%2F10.1086%2F351880&rft.aulast=Hanle&rft.aufirst=P.A.&rfr_id=info%3Asid%2Fmk.wikipedia.org%3A%D0%91%D1%80%D0%B0%D0%BD%D0%BE%D0%B2%D0%B0+%D1%84%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D1%98%D0%B0" class="Z3988"></span><span class="cs1-maint citation-comment">CS1-одржување: ref=harv (<a href="/wiki/%D0%9A%D0%B0%D1%82%D0%B5%D0%B3%D0%BE%D1%80%D0%B8%D1%98%D0%B0:CS1-%D0%BE%D0%B4%D1%80%D0%B6%D1%83%D0%B2%D0%B0%D1%9A%D0%B5:_ref%3Dharv" title="Категорија:CS1-одржување: ref=harv">link</a>)</span><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r5289462"></li> <li><cite id="CITEREFJaynes2003" class="citation book">Jaynes, E. T. (2003). G. Larry Bretthorst (уред.). <i>Probability Theory: The Logic of Science</i>. Cambridge University Press. <a href="/wiki/ISBN" title="ISBN">ISBN</a> <a href="/wiki/%D0%A1%D0%BF%D0%B5%D1%86%D0%B8%D1%98%D0%B0%D0%BB%D0%BD%D0%B0:%D0%9F%D0%B5%D1%87%D0%B0%D1%82%D0%B5%D0%BD%D0%98%D0%B7%D0%B2%D0%BE%D1%80/978-0-521_59271-0" title="Специјална:ПечатенИзвор/978-0-521 59271-0"><bdi>978-0-521 59271-0</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Probability+Theory%3A+The+Logic+of+Science&rft.pub=Cambridge+University+Press&rft.date=2003&rft.isbn=978-0-52159271-0&rft.aulast=Jaynes&rft.aufirst=E.+T.&rfr_id=info%3Asid%2Fmk.wikipedia.org%3A%D0%91%D1%80%D0%B0%D0%BD%D0%BE%D0%B2%D0%B0+%D1%84%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D1%98%D0%B0" class="Z3988"></span><span class="cs1-maint citation-comment">CS1-одржување: ref=harv (<a href="/wiki/%D0%9A%D0%B0%D1%82%D0%B5%D0%B3%D0%BE%D1%80%D0%B8%D1%98%D0%B0:CS1-%D0%BE%D0%B4%D1%80%D0%B6%D1%83%D0%B2%D0%B0%D1%9A%D0%B5:_ref%3Dharv" title="Категорија:CS1-одржување: ref=harv">link</a>)</span><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r5289462"></li> <li><cite id="CITEREFLandauLifshitz1977" class="citation book"><a href="/w/index.php?title=Lev_Landau&action=edit&redlink=1" class="new" title="Lev Landau (страницата не постои)">Landau, L.D.</a>; <a href="/w/index.php?title=Evgeny_Lifshitz&action=edit&redlink=1" class="new" title="Evgeny Lifshitz (страницата не постои)">Lifshitz, E. M.</a> (1977). <i>Quantum Mechanics: Non-Relativistic Theory</i>. Vol. 3 (3. изд.). <a href="/w/index.php?title=Pergamon_Press&action=edit&redlink=1" class="new" title="Pergamon Press (страницата не постои)">Pergamon Press</a>. <a href="/wiki/ISBN" title="ISBN">ISBN</a> <a href="/wiki/%D0%A1%D0%BF%D0%B5%D1%86%D0%B8%D1%98%D0%B0%D0%BB%D0%BD%D0%B0:%D0%9F%D0%B5%D1%87%D0%B0%D1%82%D0%B5%D0%BD%D0%98%D0%B7%D0%B2%D0%BE%D1%80/978-0-08-020940-1" title="Специјална:ПечатенИзвор/978-0-08-020940-1"><bdi>978-0-08-020940-1</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Quantum+Mechanics%3A+Non-Relativistic+Theory&rft.edition=3&rft.pub=Pergamon+Press&rft.date=1977&rft.isbn=978-0-08-020940-1&rft.aulast=Landau&rft.aufirst=L.D.&rft.au=Lifshitz%2C+E.+M.&rfr_id=info%3Asid%2Fmk.wikipedia.org%3A%D0%91%D1%80%D0%B0%D0%BD%D0%BE%D0%B2%D0%B0+%D1%84%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D1%98%D0%B0" class="Z3988"></span><span class="cs1-maint citation-comment">CS1-одржување: ref=harv (<a href="/wiki/%D0%9A%D0%B0%D1%82%D0%B5%D0%B3%D0%BE%D1%80%D0%B8%D1%98%D0%B0:CS1-%D0%BE%D0%B4%D1%80%D0%B6%D1%83%D0%B2%D0%B0%D1%9A%D0%B5:_ref%3Dharv" title="Категорија:CS1-одржување: ref=harv">link</a>)</span><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r5289462"> <a rel="nofollow" class="external text" href="https://archive.org/details/QuantumMechanics_104">Online copy</a></li> <li><cite id="CITEREFLernerTrigg1991" class="citation book">Lerner, R.G.; Trigg, G.L. (1991). <a rel="nofollow" class="external text" href="https://archive.org/details/encyclopediaofph00lern"><i>Encyclopaedia of Physics</i></a> (2. изд.). VHC Publishers. <a href="/wiki/ISBN" title="ISBN">ISBN</a> <a href="/wiki/%D0%A1%D0%BF%D0%B5%D1%86%D0%B8%D1%98%D0%B0%D0%BB%D0%BD%D0%B0:%D0%9F%D0%B5%D1%87%D0%B0%D1%82%D0%B5%D0%BD%D0%98%D0%B7%D0%B2%D0%BE%D1%80/978-0-89573-752-6" title="Специјална:ПечатенИзвор/978-0-89573-752-6"><bdi>978-0-89573-752-6</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Encyclopaedia+of+Physics&rft.edition=2&rft.pub=VHC+Publishers&rft.date=1991&rft.isbn=978-0-89573-752-6&rft.aulast=Lerner&rft.aufirst=R.G.&rft.au=Trigg%2C+G.L.&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fencyclopediaofph00lern&rfr_id=info%3Asid%2Fmk.wikipedia.org%3A%D0%91%D1%80%D0%B0%D0%BD%D0%BE%D0%B2%D0%B0+%D1%84%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D1%98%D0%B0" class="Z3988"></span><span class="cs1-maint citation-comment">CS1-одржување: ref=harv (<a href="/wiki/%D0%9A%D0%B0%D1%82%D0%B5%D0%B3%D0%BE%D1%80%D0%B8%D1%98%D0%B0:CS1-%D0%BE%D0%B4%D1%80%D0%B6%D1%83%D0%B2%D0%B0%D1%9A%D0%B5:_ref%3Dharv" title="Категорија:CS1-одржување: ref=harv">link</a>)</span><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r5289462"></li> <li><cite id="CITEREFLudwig1968" class="citation book">Ludwig, G. (1968). <a rel="nofollow" class="external text" href="https://archive.org/details/wavemechanics0000ludw"><i>Wave Mechanics</i></a>. Oxford UK: Pergamon Press. <a href="/wiki/ISBN" title="ISBN">ISBN</a> <a href="/wiki/%D0%A1%D0%BF%D0%B5%D1%86%D0%B8%D1%98%D0%B0%D0%BB%D0%BD%D0%B0:%D0%9F%D0%B5%D1%87%D0%B0%D1%82%D0%B5%D0%BD%D0%98%D0%B7%D0%B2%D0%BE%D1%80/978-0-08-203204-5" title="Специјална:ПечатенИзвор/978-0-08-203204-5"><bdi>978-0-08-203204-5</bdi></a>. <a href="/wiki/LCCN" class="mw-redirect" title="LCCN">LCCN</a> <a rel="nofollow" class="external text" href="//lccn.loc.gov/66-30631">66-30631</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Wave+Mechanics&rft.place=Oxford+UK&rft.pub=Pergamon+Press&rft.date=1968&rft_id=info%3Alccn%2F66-30631&rft.isbn=978-0-08-203204-5&rft.aulast=Ludwig&rft.aufirst=G.&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fwavemechanics0000ludw&rfr_id=info%3Asid%2Fmk.wikipedia.org%3A%D0%91%D1%80%D0%B0%D0%BD%D0%BE%D0%B2%D0%B0+%D1%84%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D1%98%D0%B0" class="Z3988"></span><span class="cs1-maint citation-comment">CS1-одржување: ref=harv (<a href="/wiki/%D0%9A%D0%B0%D1%82%D0%B5%D0%B3%D0%BE%D1%80%D0%B8%D1%98%D0%B0:CS1-%D0%BE%D0%B4%D1%80%D0%B6%D1%83%D0%B2%D0%B0%D1%9A%D0%B5:_ref%3Dharv" title="Категорија:CS1-одржување: ref=harv">link</a>)</span><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r5289462"></li> <li><cite id="CITEREFMurdoch1987" class="citation book">Murdoch, D. (1987). <a rel="nofollow" class="external text" href="https://archive.org/details/nielsbohrsphilos0000murd"><i>Niels Bohr's Philosophy of Physics</i></a>. Cambridge UK: Cambridge University Press. <a href="/wiki/ISBN" title="ISBN">ISBN</a> <a href="/wiki/%D0%A1%D0%BF%D0%B5%D1%86%D0%B8%D1%98%D0%B0%D0%BB%D0%BD%D0%B0:%D0%9F%D0%B5%D1%87%D0%B0%D1%82%D0%B5%D0%BD%D0%98%D0%B7%D0%B2%D0%BE%D1%80/978-0-521-33320-7" title="Специјална:ПечатенИзвор/978-0-521-33320-7"><bdi>978-0-521-33320-7</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Niels+Bohr%27s+Philosophy+of+Physics&rft.place=Cambridge+UK&rft.pub=Cambridge+University+Press&rft.date=1987&rft.isbn=978-0-521-33320-7&rft.aulast=Murdoch&rft.aufirst=D.&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fnielsbohrsphilos0000murd&rfr_id=info%3Asid%2Fmk.wikipedia.org%3A%D0%91%D1%80%D0%B0%D0%BD%D0%BE%D0%B2%D0%B0+%D1%84%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D1%98%D0%B0" class="Z3988"></span><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r5289462"></li> <li><cite id="CITEREFNewton2002" class="citation book">Newton, R.G. (2002). <i>Quantum Physics: a Text for Graduate Student</i>. New York: Springer. <a href="/wiki/ISBN" title="ISBN">ISBN</a> <a href="/wiki/%D0%A1%D0%BF%D0%B5%D1%86%D0%B8%D1%98%D0%B0%D0%BB%D0%BD%D0%B0:%D0%9F%D0%B5%D1%87%D0%B0%D1%82%D0%B5%D0%BD%D0%98%D0%B7%D0%B2%D0%BE%D1%80/978-0-387-95473-8" title="Специјална:ПечатенИзвор/978-0-387-95473-8"><bdi>978-0-387-95473-8</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Quantum+Physics%3A+a+Text+for+Graduate+Student&rft.place=New+York&rft.pub=Springer&rft.date=2002&rft.isbn=978-0-387-95473-8&rft.aulast=Newton&rft.aufirst=R.G.&rfr_id=info%3Asid%2Fmk.wikipedia.org%3A%D0%91%D1%80%D0%B0%D0%BD%D0%BE%D0%B2%D0%B0+%D1%84%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D1%98%D0%B0" class="Z3988"></span><span class="cs1-maint citation-comment">CS1-одржување: ref=harv (<a href="/wiki/%D0%9A%D0%B0%D1%82%D0%B5%D0%B3%D0%BE%D1%80%D0%B8%D1%98%D0%B0:CS1-%D0%BE%D0%B4%D1%80%D0%B6%D1%83%D0%B2%D0%B0%D1%9A%D0%B5:_ref%3Dharv" title="Категорија:CS1-одржување: ref=harv">link</a>)</span><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r5289462"></li> <li><cite id="CITEREFPauli1927" class="citation journal"><a href="/w/index.php?title=Wolfgang_Pauli&action=edit&redlink=1" class="new" title="Wolfgang Pauli (страницата не постои)">Pauli, Wolfgang</a> (1927). „Zur Quantenmechanik des magnetischen Elektrons“. <i>Zeitschrift für Physik</i> (германски). <b>43</b> (9–10): 601–623. <a href="/wiki/Bibcode" title="Bibcode">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1927ZPhy...43..601P">1927ZPhy...43..601P</a>. <a href="/wiki/Doi" class="mw-redirect" title="Doi">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2Fbf01397326">10.1007/bf01397326</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Zeitschrift+f%C3%BCr+Physik&rft.atitle=Zur+Quantenmechanik+des+magnetischen+Elektrons&rft.volume=43&rft.issue=9%E2%80%9310&rft.pages=601-623&rft.date=1927&rft_id=info%3Adoi%2F10.1007%2Fbf01397326&rft_id=info%3Abibcode%2F1927ZPhy...43..601P&rft.aulast=Pauli&rft.aufirst=Wolfgang&rfr_id=info%3Asid%2Fmk.wikipedia.org%3A%D0%91%D1%80%D0%B0%D0%BD%D0%BE%D0%B2%D0%B0+%D1%84%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D1%98%D0%B0" class="Z3988"></span><span class="cs1-maint citation-comment">CS1-одржување: ref=harv (<a href="/wiki/%D0%9A%D0%B0%D1%82%D0%B5%D0%B3%D0%BE%D1%80%D0%B8%D1%98%D0%B0:CS1-%D0%BE%D0%B4%D1%80%D0%B6%D1%83%D0%B2%D0%B0%D1%9A%D0%B5:_ref%3Dharv" title="Категорија:CS1-одржување: ref=harv">link</a>)</span><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r5289462"></li> <li><cite id="CITEREFPelegPniniZaarurHecht2010" class="citation book">Peleg, Y.; Pnini, R.; Zaarur, E.; Hecht, E. (2010). <i>Quantum mechanics</i>. Schaum's outlines (2. изд.). McGraw Hill. <a href="/wiki/ISBN" title="ISBN">ISBN</a> <a href="/wiki/%D0%A1%D0%BF%D0%B5%D1%86%D0%B8%D1%98%D0%B0%D0%BB%D0%BD%D0%B0:%D0%9F%D0%B5%D1%87%D0%B0%D1%82%D0%B5%D0%BD%D0%98%D0%B7%D0%B2%D0%BE%D1%80/978-0-07-162358-2" title="Специјална:ПечатенИзвор/978-0-07-162358-2"><bdi>978-0-07-162358-2</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Quantum+mechanics&rft.series=Schaum%27s+outlines&rft.edition=2&rft.pub=McGraw+Hill&rft.date=2010&rft.isbn=978-0-07-162358-2&rft.aulast=Peleg&rft.aufirst=Y.&rft.au=Pnini%2C+R.&rft.au=Zaarur%2C+E.&rft.au=Hecht%2C+E.&rfr_id=info%3Asid%2Fmk.wikipedia.org%3A%D0%91%D1%80%D0%B0%D0%BD%D0%BE%D0%B2%D0%B0+%D1%84%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D1%98%D0%B0" class="Z3988"></span><span class="cs1-maint citation-comment">CS1-одржување: ref=harv (<a href="/wiki/%D0%9A%D0%B0%D1%82%D0%B5%D0%B3%D0%BE%D1%80%D0%B8%D1%98%D0%B0:CS1-%D0%BE%D0%B4%D1%80%D0%B6%D1%83%D0%B2%D0%B0%D1%9A%D0%B5:_ref%3Dharv" title="Категорија:CS1-одржување: ref=harv">link</a>)</span><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r5289462"></li> <li><cite id="CITEREFRae2008" class="citation book">Rae, A.I.M. (2008). <a rel="nofollow" class="external text" href="https://books.google.com/?id=YDhHAQAAIAAJ&q=quantum+mechanics+Alastair+Rae+5th+edition&dq=quantum+mechanics+Alastair+Rae+5th+edition"><i>Quantum Mechanics</i></a>. <b>2</b> (5. изд.). Taylor & Francis Group. <a href="/wiki/ISBN" title="ISBN">ISBN</a> <a href="/wiki/%D0%A1%D0%BF%D0%B5%D1%86%D0%B8%D1%98%D0%B0%D0%BB%D0%BD%D0%B0:%D0%9F%D0%B5%D1%87%D0%B0%D1%82%D0%B5%D0%BD%D0%98%D0%B7%D0%B2%D0%BE%D1%80/978-1-5848-89700" title="Специјална:ПечатенИзвор/978-1-5848-89700"><bdi>978-1-5848-89700</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Quantum+Mechanics&rft.edition=5&rft.pub=Taylor+%26+Francis+Group&rft.date=2008&rft.isbn=978-1-5848-89700&rft.aulast=Rae&rft.aufirst=A.I.M.&rft_id=https%3A%2F%2Fbooks.google.com%2F%3Fid%3DYDhHAQAAIAAJ%26q%3Dquantum%2Bmechanics%2BAlastair%2BRae%2B5th%2Bedition%26dq%3Dquantum%2Bmechanics%2BAlastair%2BRae%2B5th%2Bedition&rfr_id=info%3Asid%2Fmk.wikipedia.org%3A%D0%91%D1%80%D0%B0%D0%BD%D0%BE%D0%B2%D0%B0+%D1%84%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D1%98%D0%B0" class="Z3988"></span><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r5289462"></li> <li><cite id="CITEREFSchrödinger1926" class="citation journal"><a href="/w/index.php?title=Erwin_Schr%C3%B6dinger&action=edit&redlink=1" class="new" title="Erwin Schrödinger (страницата не постои)">Schrödinger, E.</a> (1926). <a rel="nofollow" class="external text" href="https://web.archive.org/web/20081217040121/http://home.tiscali.nl/physis/HistoricPaper/Schroedinger/Schroedinger1926c.pdf">„An Undulatory Theory of the Mechanics of Atoms and Molecules“</a> <span class="cs1-format">(PDF)</span>. <i>Physical Review</i>. <b>28</b> (6): 1049–1070. <a href="/wiki/Bibcode" title="Bibcode">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1926PhRv...28.1049S">1926PhRv...28.1049S</a>. <a href="/wiki/Doi" class="mw-redirect" title="Doi">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1103%2FPhysRev.28.1049">10.1103/PhysRev.28.1049</a>. Архивирано од <a rel="nofollow" class="external text" href="http://home.tiscali.nl/physis/HistoricPaper/Schroedinger/Schroedinger1926c.pdf">изворникот</a> <span class="cs1-format">(PDF)</span> на 17 декември 2008.</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.issue=6&rft.pages=1049-1070&rft.date=1926&rft_id=info%3Adoi%2F10.1103%2FPhysRev.28.1049&rft_id=info%3Abibcode%2F1926PhRv...28.1049S&rft.aulast=Schr%C3%B6dinger&rft.aufirst=E.&rft_id=http%3A%2F%2Fhome.tiscali.nl%2Fphysis%2FHistoricPaper%2FSchroedinger%2FSchroedinger1926c.pdf&rfr_id=info%3Asid%2Fmk.wikipedia.org%3A%D0%91%D1%80%D0%B0%D0%BD%D0%BE%D0%B2%D0%B0+%D1%84%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D1%98%D0%B0" class="Z3988"></span><span class="cs1-maint citation-comment">CS1-одржување: ref=harv (<a href="/wiki/%D0%9A%D0%B0%D1%82%D0%B5%D0%B3%D0%BE%D1%80%D0%B8%D1%98%D0%B0:CS1-%D0%BE%D0%B4%D1%80%D0%B6%D1%83%D0%B2%D0%B0%D1%9A%D0%B5:_ref%3Dharv" title="Категорија:CS1-одржување: ref=harv">link</a>)</span><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r5289462"></li> <li><cite id="CITEREFShankar1994" class="citation book">Shankar, R. (1994). <i>Principles of Quantum Mechanics</i> (2. изд.). <a href="/wiki/ISBN" title="ISBN">ISBN</a> <a href="/wiki/%D0%A1%D0%BF%D0%B5%D1%86%D0%B8%D1%98%D0%B0%D0%BB%D0%BD%D0%B0:%D0%9F%D0%B5%D1%87%D0%B0%D1%82%D0%B5%D0%BD%D0%98%D0%B7%D0%B2%D0%BE%D1%80/978-0306447907" title="Специјална:ПечатенИзвор/978-0306447907"><bdi>978-0306447907</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Principles+of+Quantum+Mechanics&rft.edition=2&rft.date=1994&rft.isbn=978-0306447907&rft.aulast=Shankar&rft.aufirst=R.&rfr_id=info%3Asid%2Fmk.wikipedia.org%3A%D0%91%D1%80%D0%B0%D0%BD%D0%BE%D0%B2%D0%B0+%D1%84%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D1%98%D0%B0" class="Z3988"></span><span class="cs1-maint citation-comment">CS1-одржување: ref=harv (<a href="/wiki/%D0%9A%D0%B0%D1%82%D0%B5%D0%B3%D0%BE%D1%80%D0%B8%D1%98%D0%B0:CS1-%D0%BE%D0%B4%D1%80%D0%B6%D1%83%D0%B2%D0%B0%D1%9A%D0%B5:_ref%3Dharv" title="Категорија:CS1-одржување: ref=harv">link</a>)</span><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r5289462"></li> <li><cite id="CITEREFMartinShaw2008" class="citation book">Martin, B.R.; Shaw, G. (2008). <i>Particle Physics</i>. Manchester Physics Series (3. изд.). John Wiley & Sons. <a href="/wiki/ISBN" title="ISBN">ISBN</a> <a href="/wiki/%D0%A1%D0%BF%D0%B5%D1%86%D0%B8%D1%98%D0%B0%D0%BB%D0%BD%D0%B0:%D0%9F%D0%B5%D1%87%D0%B0%D1%82%D0%B5%D0%BD%D0%98%D0%B7%D0%B2%D0%BE%D1%80/978-0-470-03294-7" title="Специјална:ПечатенИзвор/978-0-470-03294-7"><bdi>978-0-470-03294-7</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Particle+Physics&rft.series=Manchester+Physics+Series&rft.edition=3&rft.pub=John+Wiley+%26+Sons&rft.date=2008&rft.isbn=978-0-470-03294-7&rft.aulast=Martin&rft.aufirst=B.R.&rft.au=Shaw%2C+G.&rfr_id=info%3Asid%2Fmk.wikipedia.org%3A%D0%91%D1%80%D0%B0%D0%BD%D0%BE%D0%B2%D0%B0+%D1%84%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D1%98%D0%B0" class="Z3988"></span><span class="cs1-maint citation-comment">CS1-одржување: ref=harv (<a href="/wiki/%D0%9A%D0%B0%D1%82%D0%B5%D0%B3%D0%BE%D1%80%D0%B8%D1%98%D0%B0:CS1-%D0%BE%D0%B4%D1%80%D0%B6%D1%83%D0%B2%D0%B0%D1%9A%D0%B5:_ref%3Dharv" title="Категорија:CS1-одржување: ref=harv">link</a>)</span><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r5289462"></li> <li><cite id="CITEREFter_Haar1967" class="citation book"><a href="/w/index.php?title=Dirk_ter_Haar&action=edit&redlink=1" class="new" title="Dirk ter Haar (страницата не постои)">ter Haar, D.</a> (1967). <a rel="nofollow" class="external text" href="https://archive.org/details/oldquantumtheory00haar"><i>The Old Quantum Theory</i></a>. <a href="/w/index.php?title=Pergamon_Press&action=edit&redlink=1" class="new" title="Pergamon Press (страницата не постои)">Pergamon Press</a>. стр. <a rel="nofollow" class="external text" href="https://archive.org/details/oldquantumtheory00haar/page/167">167</a>–183. <a href="/wiki/LCCN" class="mw-redirect" title="LCCN">LCCN</a> <a rel="nofollow" class="external text" href="//lccn.loc.gov/66029628">66029628</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Old+Quantum+Theory&rft.pages=167-183&rft.pub=Pergamon+Press&rft.date=1967&rft_id=info%3Alccn%2F66029628&rft.aulast=ter+Haar&rft.aufirst=D.&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Foldquantumtheory00haar&rfr_id=info%3Asid%2Fmk.wikipedia.org%3A%D0%91%D1%80%D0%B0%D0%BD%D0%BE%D0%B2%D0%B0+%D1%84%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D1%98%D0%B0" class="Z3988"></span><span class="cs1-maint citation-comment">CS1-одржување: ref=harv (<a href="/wiki/%D0%9A%D0%B0%D1%82%D0%B5%D0%B3%D0%BE%D1%80%D0%B8%D1%98%D0%B0:CS1-%D0%BE%D0%B4%D1%80%D0%B6%D1%83%D0%B2%D0%B0%D1%9A%D0%B5:_ref%3Dharv" title="Категорија:CS1-одржување: ref=harv">link</a>)</span><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r5289462"></li> <li><cite id="CITEREFTiplerMoscaFreeman2008" class="citation book">Tipler, P. A.; Mosca, G.; Freeman (2008). <i>Physics for Scientists and Engineers – with Modern Physics</i> (6. изд.). <a href="/wiki/ISBN" title="ISBN">ISBN</a> <a href="/wiki/%D0%A1%D0%BF%D0%B5%D1%86%D0%B8%D1%98%D0%B0%D0%BB%D0%BD%D0%B0:%D0%9F%D0%B5%D1%87%D0%B0%D1%82%D0%B5%D0%BD%D0%98%D0%B7%D0%B2%D0%BE%D1%80/978-0-7167-8964-2" title="Специјална:ПечатенИзвор/978-0-7167-8964-2"><bdi>978-0-7167-8964-2</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Physics+for+Scientists+and+Engineers+%E2%80%93+with+Modern+Physics&rft.edition=6&rft.date=2008&rft.isbn=978-0-7167-8964-2&rft.aulast=Tipler&rft.aufirst=P.+A.&rft.au=Mosca%2C+G.&rft.au=Freeman&rfr_id=info%3Asid%2Fmk.wikipedia.org%3A%D0%91%D1%80%D0%B0%D0%BD%D0%BE%D0%B2%D0%B0+%D1%84%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D1%98%D0%B0" class="Z3988"></span><span class="cs1-maint citation-comment">CS1-одржување: ref=harv (<a href="/wiki/%D0%9A%D0%B0%D1%82%D0%B5%D0%B3%D0%BE%D1%80%D0%B8%D1%98%D0%B0:CS1-%D0%BE%D0%B4%D1%80%D0%B6%D1%83%D0%B2%D0%B0%D1%9A%D0%B5:_ref%3Dharv" title="Категорија:CS1-одржување: ref=harv">link</a>)</span><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r5289462"></li> <li><cite id="CITEREFWeinberg2013" class="citation"><a href="/w/index.php?title=Steven_Weinberg&action=edit&redlink=1" class="new" title="Steven Weinberg (страницата не постои)">Weinberg, S.</a> (2013), <i>Lectures in Quantum Mechanics</i>, Cambridge University Press, <a href="/wiki/ISBN" title="ISBN">ISBN</a> <a href="/wiki/%D0%A1%D0%BF%D0%B5%D1%86%D0%B8%D1%98%D0%B0%D0%BB%D0%BD%D0%B0:%D0%9F%D0%B5%D1%87%D0%B0%D1%82%D0%B5%D0%BD%D0%98%D0%B7%D0%B2%D0%BE%D1%80/978-1-107-02872-2" title="Специјална:ПечатенИзвор/978-1-107-02872-2"><bdi>978-1-107-02872-2</bdi></a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Lectures+in+Quantum+Mechanics&rft.pub=Cambridge+University+Press&rft.date=2013&rft.isbn=978-1-107-02872-2&rft.aulast=Weinberg&rft.aufirst=S.&rfr_id=info%3Asid%2Fmk.wikipedia.org%3A%D0%91%D1%80%D0%B0%D0%BD%D0%BE%D0%B2%D0%B0+%D1%84%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D1%98%D0%B0" class="Z3988"></span><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r5289462"></li> <li><cite id="CITEREFWeinberg2002" class="citation">Weinberg, S. (2002), <i>The Quantum Theory of Fields</i>, <b>1</b>, Cambridge University Press, <a href="/wiki/ISBN" title="ISBN">ISBN</a> <a href="/wiki/%D0%A1%D0%BF%D0%B5%D1%86%D0%B8%D1%98%D0%B0%D0%BB%D0%BD%D0%B0:%D0%9F%D0%B5%D1%87%D0%B0%D1%82%D0%B5%D0%BD%D0%98%D0%B7%D0%B2%D0%BE%D1%80/978-0-521-55001-7" title="Специјална:ПечатенИзвор/978-0-521-55001-7"><bdi>978-0-521-55001-7</bdi></a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Quantum+Theory+of+Fields&rft.pub=Cambridge+University+Press&rft.date=2002&rft.isbn=978-0-521-55001-7&rft.aulast=Weinberg&rft.aufirst=S.&rfr_id=info%3Asid%2Fmk.wikipedia.org%3A%D0%91%D1%80%D0%B0%D0%BD%D0%BE%D0%B2%D0%B0+%D1%84%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D1%98%D0%B0" class="Z3988"></span><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r5289462"></li> <li><cite id="CITEREFYoungFreedman2008" class="citation book">Young, H. D.; Freedman, R. A. (2008). Pearson (уред.). <i>Sears' and Zemansky's University Physics</i> (12. изд.). Addison-Wesley. <a href="/wiki/ISBN" title="ISBN">ISBN</a> <a href="/wiki/%D0%A1%D0%BF%D0%B5%D1%86%D0%B8%D1%98%D0%B0%D0%BB%D0%BD%D0%B0:%D0%9F%D0%B5%D1%87%D0%B0%D1%82%D0%B5%D0%BD%D0%98%D0%B7%D0%B2%D0%BE%D1%80/978-0-321-50130-1" title="Специјална:ПечатенИзвор/978-0-321-50130-1"><bdi>978-0-321-50130-1</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Sears%27+and+Zemansky%27s+University+Physics&rft.edition=12&rft.pub=Addison-Wesley&rft.date=2008&rft.isbn=978-0-321-50130-1&rft.aulast=Young&rft.aufirst=H.+D.&rft.au=Freedman%2C+R.+A.&rfr_id=info%3Asid%2Fmk.wikipedia.org%3A%D0%91%D1%80%D0%B0%D0%BD%D0%BE%D0%B2%D0%B0+%D1%84%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D1%98%D0%B0" class="Z3988"></span><span class="cs1-maint citation-comment">CS1-одржување: ref=harv (<a href="/wiki/%D0%9A%D0%B0%D1%82%D0%B5%D0%B3%D0%BE%D1%80%D0%B8%D1%98%D0%B0:CS1-%D0%BE%D0%B4%D1%80%D0%B6%D1%83%D0%B2%D0%B0%D1%9A%D0%B5:_ref%3Dharv" title="Категорија:CS1-одржување: ref=harv">link</a>)</span><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r5289462"></li> <li><cite id="CITEREFWheelerZurek1983" class="citation book"><a href="/w/index.php?title=John_Archibald_Wheeler&action=edit&redlink=1" class="new" title="John Archibald Wheeler (страницата не постои)">Wheeler, J.A.</a>; <a href="/w/index.php?title=Wojciech_H._Zurek&action=edit&redlink=1" class="new" title="Wojciech H. Zurek (страницата не постои)">Zurek, W.H.</a> (1983). <i>Quantum Theory and Measurement</i>. Princeton NJ: Princeton University Press.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Quantum+Theory+and+Measurement&rft.place=Princeton+NJ&rft.pub=Princeton+University+Press&rft.date=1983&rft.aulast=Wheeler&rft.aufirst=J.A.&rft.au=Zurek%2C+W.H.&rfr_id=info%3Asid%2Fmk.wikipedia.org%3A%D0%91%D1%80%D0%B0%D0%BD%D0%BE%D0%B2%D0%B0+%D1%84%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D1%98%D0%B0" class="Z3988"></span><span class="cs1-maint citation-comment">CS1-одржување: ref=harv (<a href="/wiki/%D0%9A%D0%B0%D1%82%D0%B5%D0%B3%D0%BE%D1%80%D0%B8%D1%98%D0%B0:CS1-%D0%BE%D0%B4%D1%80%D0%B6%D1%83%D0%B2%D0%B0%D1%9A%D0%B5:_ref%3Dharv" title="Категорија:CS1-одржување: ref=harv">link</a>)</span><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r5289462"></li> <li><cite id="CITEREFZettili2009" class="citation book">Zettili, N. (2009). <i>Quantum Mechanics: Concepts and Applications</i> (2. изд.). <a href="/wiki/ISBN" title="ISBN">ISBN</a> <a href="/wiki/%D0%A1%D0%BF%D0%B5%D1%86%D0%B8%D1%98%D0%B0%D0%BB%D0%BD%D0%B0:%D0%9F%D0%B5%D1%87%D0%B0%D1%82%D0%B5%D0%BD%D0%98%D0%B7%D0%B2%D0%BE%D1%80/978-0-470-02679-3" title="Специјална:ПечатенИзвор/978-0-470-02679-3"><bdi>978-0-470-02679-3</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Quantum+Mechanics%3A+Concepts+and+Applications&rft.edition=2&rft.date=2009&rft.isbn=978-0-470-02679-3&rft.aulast=Zettili&rft.aufirst=N.&rfr_id=info%3Asid%2Fmk.wikipedia.org%3A%D0%91%D1%80%D0%B0%D0%BD%D0%BE%D0%B2%D0%B0+%D1%84%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D1%98%D0%B0" class="Z3988"></span><span class="cs1-maint citation-comment">CS1-одржување: ref=harv (<a href="/wiki/%D0%9A%D0%B0%D1%82%D0%B5%D0%B3%D0%BE%D1%80%D0%B8%D1%98%D0%B0:CS1-%D0%BE%D0%B4%D1%80%D0%B6%D1%83%D0%B2%D0%B0%D1%9A%D0%B5:_ref%3Dharv" title="Категорија:CS1-одржување: ref=harv">link</a>)</span><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r5289462"></li> <li><cite id="CITEREFZwiebach2009" class="citation book">Zwiebach, Barton (2009). <i>A First Course in String Theory</i>. Cambridge University Press. <a href="/wiki/ISBN" title="ISBN">ISBN</a> <a href="/wiki/%D0%A1%D0%BF%D0%B5%D1%86%D0%B8%D1%98%D0%B0%D0%BB%D0%BD%D0%B0:%D0%9F%D0%B5%D1%87%D0%B0%D1%82%D0%B5%D0%BD%D0%98%D0%B7%D0%B2%D0%BE%D1%80/978-0-521-88032-9" title="Специјална:ПечатенИзвор/978-0-521-88032-9"><bdi>978-0-521-88032-9</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=A+First+Course+in+String+Theory&rft.pub=Cambridge+University+Press&rft.date=2009&rft.isbn=978-0-521-88032-9&rft.aulast=Zwiebach&rft.aufirst=Barton&rfr_id=info%3Asid%2Fmk.wikipedia.org%3A%D0%91%D1%80%D0%B0%D0%BD%D0%BE%D0%B2%D0%B0+%D1%84%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D1%98%D0%B0" class="Z3988"></span><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r5289462"></li> <li><cite id="CITEREFYong-Ki_Kim2000" class="citation journal">Yong-Ki Kim (2 септември 2000). <a rel="nofollow" class="external text" href="https://web.archive.org/web/20110722141558/http://amods.kaeri.re.kr/mcdf/lectnote.pdf">„Practical Atomic Physics“</a> <span class="cs1-format">(PDF)</span>. <i>National Institute of Standards and Technology</i>: 1 (55 pages). Архивирано од <a rel="nofollow" class="external text" href="http://amods.kaeri.re.kr/mcdf/lectnote.pdf">изворникот</a> <span class="cs1-format">(PDF)</span> на 22 јули 2011<span class="reference-accessdate">. Посетено на 17 август 2010</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=National+Institute+of+Standards+and+Technology&rft.atitle=Practical+Atomic+Physics&rft.pages=1+%2855+pages%29&rft.date=2000-09-02&rft.au=Yong-Ki+Kim&rft_id=http%3A%2F%2Famods.kaeri.re.kr%2Fmcdf%2Flectnote.pdf&rfr_id=info%3Asid%2Fmk.wikipedia.org%3A%D0%91%D1%80%D0%B0%D0%BD%D0%BE%D0%B2%D0%B0+%D1%84%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D1%98%D0%B0" class="Z3988"></span><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r5289462"></li> <li><cite id="CITEREFPolkinghorne,_John2002" class="citation book"><a href="/w/index.php?title=John_Polkinghorne&action=edit&redlink=1" class="new" title="John Polkinghorne (страницата не постои)">Polkinghorne, John</a> (2002). <i>Quantum Theory, A Very Short Introduction</i>. Oxford University Press. <a href="/wiki/ISBN" title="ISBN">ISBN</a> <a href="/wiki/%D0%A1%D0%BF%D0%B5%D1%86%D0%B8%D1%98%D0%B0%D0%BB%D0%BD%D0%B0:%D0%9F%D0%B5%D1%87%D0%B0%D1%82%D0%B5%D0%BD%D0%98%D0%B7%D0%B2%D0%BE%D1%80/978-0-19-280252-1" title="Специјална:ПечатенИзвор/978-0-19-280252-1"><bdi>978-0-19-280252-1</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Quantum+Theory%2C+A+Very+Short+Introduction&rft.pub=Oxford+University+Press&rft.date=2002&rft.isbn=978-0-19-280252-1&rft.au=Polkinghorne%2C+John&rfr_id=info%3Asid%2Fmk.wikipedia.org%3A%D0%91%D1%80%D0%B0%D0%BD%D0%BE%D0%B2%D0%B0+%D1%84%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D1%98%D0%B0" class="Z3988"></span><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r5289462"></li></ul> </div><p>  </p><div class="mw-heading mw-heading2"><h2 id="Надворешни_врски"><span id=".D0.9D.D0.B0.D0.B4.D0.B2.D0.BE.D1.80.D0.B5.D1.88.D0.BD.D0.B8_.D0.B2.D1.80.D1.81.D0.BA.D0.B8"></span>Надворешни врски</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D0%91%D1%80%D0%B0%D0%BD%D0%BE%D0%B2%D0%B0_%D1%84%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D1%98%D0%B0&veaction=edit&section=12" title="Уреди го одделот „Надворешни врски“" class="mw-editsection-visualeditor"><span>уреди</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%D0%91%D1%80%D0%B0%D0%BD%D0%BE%D0%B2%D0%B0_%D1%84%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D1%98%D0%B0&action=edit&section=12" title="Уреди изворен код на одделот: Надворешни врски"><span>уреди извор</span></a><span class="mw-editsection-bracket">]</span></span></div> <table role="presentation" class="mbox-small plainlinks sistersitebox" style="background-color:var(--background-color-neutral-subtle, #f8f9fa);border:1px solid var(--border-color-base, #a2a9b1);color:inherit"> <tbody><tr> <td class="mbox-image"><span typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/30px-Commons-logo.svg.png" decoding="async" width="30" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/45px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/59px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></span></span></td> <td class="mbox-text plainlist">„<span class="plainlinks"><a class="external text" href="https://commons.wikimedia.org/wiki/Category:Wave_function?uselang=mk">Бранова функција</a>“ на Ризницата <sup><a href="/wiki/%D0%A0%D0%B8%D0%B7%D0%BD%D0%B8%D1%86%D0%B0_(%D0%92%D0%B8%D0%BA%D0%B8%D0%BC%D0%B5%D0%B4%D0%B8%D1%98%D0%B0)" title="Ризница (Викимедија)">?</a></sup></span></td></tr></tbody></table> <ul><li><a rel="nofollow" class="external text" href="http://www.eng.fsu.edu/~dommelen/quantum/style_a/complexs.html">Quantum Mechanics for Engineers</a></li> <li><a rel="nofollow" class="external text" href="http://www.nyu.edu/classes/tuckerman/adv.chem/lectures/lecture_9/node2.html">Spin wave functions NYU</a></li> <li><a rel="nofollow" class="external text" href="http://galileo.phys.virginia.edu/classes/752.mf1i.spring03/IdenticalParticlesRevisited.htm">Identical Particles Revisited, Michael Fowler</a></li> <li><a rel="nofollow" class="external text" href="http://vergil.chemistry.gatech.edu/notes/quantrev/node34.html">The Nature of Many-Electron Wavefunctions</a></li> <li><a rel="nofollow" class="external text" href="https://www.edx.org/courses/BerkeleyX/CS191x/2013_Spring/about">Quantum Mechanics and Quantum Computation at BerkeleyX</a><small><a rel="nofollow" class="external text" href="https://web.archive.org/web/20130513055801/https://www.edx.org/courses/BerkeleyX/CS191x/2013_Spring/about">Архивирано</a> на 13 мај 2013 г.</small></li> <li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20110723012756/http://astro1.panet.utoledo.edu/~ljc/einstein_ab.pdf">Einstein, <i>The quantum theory of radiation</i></a></li></ul></div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" width="1" height="1" style="border: none; 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