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class=""><span>ログイン</span></a> </li> </ul> </div> </div> </div> <div id="vector-user-links-dropdown" class="vector-dropdown vector-user-menu vector-button-flush-right vector-user-menu-logged-out" title="その他の操作" > <input type="checkbox" id="vector-user-links-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-user-links-dropdown" class="vector-dropdown-checkbox " aria-label="個人用ツール" > <label id="vector-user-links-dropdown-label" for="vector-user-links-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-ellipsis mw-ui-icon-wikimedia-ellipsis"></span> <span class="vector-dropdown-label-text">個人用ツール</span> </label> <div class="vector-dropdown-content"> <div id="p-personal" class="vector-menu mw-portlet mw-portlet-personal user-links-collapsible-item" title="利用者メニュー" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport" class="user-links-collapsible-item mw-list-item"><a href="//donate.wikimedia.org/wiki/Special:FundraiserRedirector?utm_source=donate&utm_medium=sidebar&utm_campaign=C13_ja.wikipedia.org&uselang=ja"><span>寄付</span></a></li><li id="pt-createaccount" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=%E7%89%B9%E5%88%A5:%E3%82%A2%E3%82%AB%E3%82%A6%E3%83%B3%E3%83%88%E4%BD%9C%E6%88%90&returnto=%E3%82%B9%E3%83%94%E3%83%B3%E8%BB%8C%E9%81%93%E7%9B%B8%E4%BA%92%E4%BD%9C%E7%94%A8" title="アカウントを作成してログインすることをお勧めしますが、必須ではありません"><span class="vector-icon mw-ui-icon-userAdd mw-ui-icon-wikimedia-userAdd"></span> <span>アカウント作成</span></a></li><li id="pt-login" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=%E7%89%B9%E5%88%A5:%E3%83%AD%E3%82%B0%E3%82%A4%E3%83%B3&returnto=%E3%82%B9%E3%83%94%E3%83%B3%E8%BB%8C%E9%81%93%E7%9B%B8%E4%BA%92%E4%BD%9C%E7%94%A8" title="ログインすることを推奨します。ただし、必須ではありません。 [o]" accesskey="o"><span class="vector-icon mw-ui-icon-logIn mw-ui-icon-wikimedia-logIn"></span> <span>ログイン</span></a></li> </ul> </div> </div> <div id="p-user-menu-anon-editor" class="vector-menu mw-portlet mw-portlet-user-menu-anon-editor" > <div class="vector-menu-heading"> ログアウトした編集者のページ <a href="/wiki/Wikipedia:%E3%82%A6%E3%82%A3%E3%82%AD%E3%83%9A%E3%83%87%E3%82%A3%E3%82%A2%E3%81%B8%E3%82%88%E3%81%86%E3%81%93%E3%81%9D" aria-label="編集の詳細"><span>もっと詳しく</span></a> </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-anoncontribs" class="mw-list-item"><a href="/wiki/%E7%89%B9%E5%88%A5:%E8%87%AA%E5%88%86%E3%81%AE%E6%8A%95%E7%A8%BF%E8%A8%98%E9%8C%B2" title="このIPアドレスからなされた編集の一覧 [y]" accesskey="y"><span>投稿記録</span></a></li><li id="pt-anontalk" class="mw-list-item"><a href="/wiki/%E7%89%B9%E5%88%A5:%E3%83%88%E3%83%BC%E3%82%AF%E3%83%9A%E3%83%BC%E3%82%B8" title="このIPアドレスからなされた編集についての議論 [n]" accesskey="n"><span>トーク</span></a></li> </ul> </div> </div> </div> </div> </nav> </div> </header> </div> <div class="mw-page-container"> <div class="mw-page-container-inner"> <div class="vector-sitenotice-container"> <div id="siteNotice"></div> </div> <div class="vector-column-start"> <div class="vector-main-menu-container"> <div id="mw-navigation"> <nav id="mw-panel" class="vector-main-menu-landmark" aria-label="サイト"> <div id="vector-main-menu-pinned-container" class="vector-pinned-container"> </div> </nav> </div> </div> <div class="vector-sticky-pinned-container"> <nav id="mw-panel-toc" aria-label="目次" data-event-name="ui.sidebar-toc" class="mw-table-of-contents-container vector-toc-landmark"> <div id="vector-toc-pinned-container" class="vector-pinned-container"> <div id="vector-toc" class="vector-toc vector-pinnable-element"> <div class="vector-pinnable-header vector-toc-pinnable-header vector-pinnable-header-pinned" data-feature-name="toc-pinned" data-pinnable-element-id="vector-toc" > <h2 class="vector-pinnable-header-label">目次</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">サイドバーに移動</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">非表示</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">ページ先頭</div> </a> </li> <li id="toc-古典的な説明" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#古典的な説明"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>古典的な説明</span> </div> </a> <ul id="toc-古典的な説明-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-具体的な表式" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#具体的な表式"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>具体的な表式</span> </div> </a> <ul id="toc-具体的な表式-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-スピン軌道分裂" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#スピン軌道分裂"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>スピン軌道分裂</span> </div> </a> <ul id="toc-スピン軌道分裂-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-関連項目" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#関連項目"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>関連項目</span> </div> </a> <ul id="toc-関連項目-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-参考文献" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#参考文献"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>参考文献</span> </div> </a> <ul id="toc-参考文献-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="目次" 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="目次の表示・非表示を切り替え" > <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">目次の表示・非表示を切り替え</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">スピン軌道相互作用</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="特定の記事の別の言語版に移動します。利用可能な言語18件" > <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-18" 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">18の言語版</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%AA%D8%A2%D8%AB%D8%B1_%D9%85%D8%BA%D8%B2%D9%84%D9%8A_%D9%85%D8%AF%D8%A7%D8%B1%D9%8A" title="アラビア語: تآثر مغزلي مداري" lang="ar" hreflang="ar" data-title="تآثر مغزلي مداري" data-language-autonym="العربية" data-language-local-name="アラビア語" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%A1%D0%BF%D0%B8%D0%BD-%D0%BE%D1%80%D0%B1%D0%B8%D1%82%D0%B0%D0%BB%D0%BD%D0%BE_%D0%B2%D0%B7%D0%B0%D0%B8%D0%BC%D0%BE%D0%B4%D0%B5%D0%B9%D1%81%D1%82%D0%B2%D0%B8%D0%B5" title="ブルガリア語: Спин-орбитално взаимодействие" lang="bg" hreflang="bg" data-title="Спин-орбитално взаимодействие" data-language-autonym="Български" data-language-local-name="ブルガリア語" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Interacci%C3%B3_esp%C3%ADn-%C3%B2rbita" title="カタロニア語: Interacció espín-òrbita" lang="ca" hreflang="ca" data-title="Interacció espín-òrbita" data-language-autonym="Català" data-language-local-name="カタロニア語" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Spin-Bahn-Kopplung" title="ドイツ語: Spin-Bahn-Kopplung" lang="de" hreflang="de" data-title="Spin-Bahn-Kopplung" data-language-autonym="Deutsch" data-language-local-name="ドイツ語" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Spin%E2%80%93orbit_interaction" title="英語: Spin–orbit interaction" lang="en" hreflang="en" data-title="Spin–orbit interaction" data-language-autonym="English" data-language-local-name="英語" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Interaction_spin-orbite" title="フランス語: Interaction spin-orbite" lang="fr" hreflang="fr" data-title="Interaction spin-orbite" data-language-autonym="Français" data-language-local-name="フランス語" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Interaksi_spin%E2%80%93orbit" title="インドネシア語: Interaksi spin–orbit" lang="id" hreflang="id" data-title="Interaksi spin–orbit" data-language-autonym="Bahasa Indonesia" data-language-local-name="インドネシア語" 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/Interazione_spin-orbita" title="イタリア語: Interazione spin-orbita" lang="it" hreflang="it" data-title="Interazione spin-orbita" data-language-autonym="Italiano" data-language-local-name="イタリア語" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%8A%A4%ED%95%80-%EA%B6%A4%EB%8F%84_%EC%83%81%ED%98%B8%EC%9E%91%EC%9A%A9" title="韓国語: 스핀-궤도 상호작용" lang="ko" hreflang="ko" data-title="스핀-궤도 상호작용" data-language-autonym="한국어" data-language-local-name="韓国語" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Tindak_balas_spin-petala" title="マレー語: Tindak balas spin-petala" lang="ms" hreflang="ms" data-title="Tindak balas spin-petala" data-language-autonym="Bahasa Melayu" data-language-local-name="マレー語" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Sprz%C4%99%C5%BCenie_spinowo-orbitalne" title="ポーランド語: Sprzężenie spinowo-orbitalne" lang="pl" hreflang="pl" data-title="Sprzężenie spinowo-orbitalne" data-language-autonym="Polski" data-language-local-name="ポーランド語" 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/Intera%C3%A7%C3%A3o_spin-%C3%B3rbita" title="ポルトガル語: Interação spin-órbita" lang="pt" hreflang="pt" data-title="Interação spin-órbita" data-language-autonym="Português" data-language-local-name="ポルトガル語" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%A1%D0%BF%D0%B8%D0%BD-%D0%BE%D1%80%D0%B1%D0%B8%D1%82%D0%B0%D0%BB%D1%8C%D0%BD%D0%BE%D0%B5_%D0%B2%D0%B7%D0%B0%D0%B8%D0%BC%D0%BE%D0%B4%D0%B5%D0%B9%D1%81%D1%82%D0%B2%D0%B8%D0%B5" title="ロシア語: Спин-орбитальное взаимодействие" lang="ru" hreflang="ru" data-title="Спин-орбитальное взаимодействие" data-language-autonym="Русский" data-language-local-name="ロシア語" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%AD%E0%B8%B1%E0%B8%99%E0%B8%95%E0%B8%A3%E0%B8%81%E0%B8%B4%E0%B8%A3%E0%B8%B4%E0%B8%A2%E0%B8%B2%E0%B8%82%E0%B8%AD%E0%B8%87%E0%B8%AA%E0%B8%9B%E0%B8%B4%E0%B8%99%E0%B8%81%E0%B8%B1%E0%B8%9A%E0%B8%AD%E0%B8%AD%E0%B8%A3%E0%B9%8C%E0%B8%9A%E0%B8%B4%E0%B8%97" title="タイ語: อันตรกิริยาของสปินกับออร์บิท" lang="th" hreflang="th" data-title="อันตรกิริยาของสปินกับออร์บิท" data-language-autonym="ไทย" data-language-local-name="タイ語" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Spin-y%C3%B6r%C3%BCnge_etkile%C5%9Fimi" title="トルコ語: Spin-yörünge etkileşimi" lang="tr" hreflang="tr" data-title="Spin-yörünge etkileşimi" data-language-autonym="Türkçe" data-language-local-name="トルコ語" 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%A1%D0%BF%D1%96%D0%BD-%D0%BE%D1%80%D0%B1%D1%96%D1%82%D0%B0%D0%BB%D1%8C%D0%BD%D0%B0_%D0%B2%D0%B7%D0%B0%D1%94%D0%BC%D0%BE%D0%B4%D1%96%D1%8F" title="ウクライナ語: Спін-орбітальна взаємодія" lang="uk" hreflang="uk" data-title="Спін-орбітальна взаємодія" data-language-autonym="Українська" data-language-local-name="ウクライナ語" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Spin-orbital_ta%CA%BCsir" title="ウズベク語: Spin-orbital taʼsir" lang="uz" hreflang="uz" data-title="Spin-orbital taʼsir" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="ウズベク語" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E8%87%AA%E6%97%8B-%E8%BB%8C%E9%81%93%E4%BD%9C%E7%94%A8" title="中国語: 自旋-軌道作用" lang="zh" hreflang="zh" data-title="自旋-軌道作用" data-language-autonym="中文" data-language-local-name="中国語" 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/Q1570979#sitelinks-wikipedia" title="言語間リンクを編集" class="wbc-editpage">リンクを編集</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="名前空間"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-associated-pages" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-nstab-main" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/%E3%82%B9%E3%83%94%E3%83%B3%E8%BB%8C%E9%81%93%E7%9B%B8%E4%BA%92%E4%BD%9C%E7%94%A8" title="本文を閲覧 [c]" accesskey="c"><span>ページ</span></a></li><li id="ca-talk" class="new vector-tab-noicon mw-list-item"><a href="/w/index.php?title=%E3%83%8E%E3%83%BC%E3%83%88:%E3%82%B9%E3%83%94%E3%83%B3%E8%BB%8C%E9%81%93%E7%9B%B8%E4%BA%92%E4%BD%9C%E7%94%A8&action=edit&redlink=1" rel="discussion" class="new" title="「本文ページについての議論」 (存在しないページ) [t]" accesskey="t"><span>ノート</span></a></li> </ul> </div> </div> <div id="vector-variants-dropdown" class="vector-dropdown emptyPortlet" > <input type="checkbox" id="vector-variants-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-variants-dropdown" class="vector-dropdown-checkbox " aria-label="別の言語に切り替える" > <label id="vector-variants-dropdown-label" for="vector-variants-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" ><span class="vector-dropdown-label-text">日本語</span> </label> <div class="vector-dropdown-content"> <div id="p-variants" class="vector-menu mw-portlet mw-portlet-variants emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> </div> </div> </nav> </div> <div id="right-navigation" class="vector-collapsible"> <nav aria-label="表示"> <div id="p-views" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-views" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-view" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/%E3%82%B9%E3%83%94%E3%83%B3%E8%BB%8C%E9%81%93%E7%9B%B8%E4%BA%92%E4%BD%9C%E7%94%A8"><span>閲覧</span></a></li><li id="ca-edit" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=%E3%82%B9%E3%83%94%E3%83%B3%E8%BB%8C%E9%81%93%E7%9B%B8%E4%BA%92%E4%BD%9C%E7%94%A8&action=edit" title="このページのソースコードを編集する [e]" accesskey="e"><span>編集</span></a></li><li id="ca-history" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=%E3%82%B9%E3%83%94%E3%83%B3%E8%BB%8C%E9%81%93%E7%9B%B8%E4%BA%92%E4%BD%9C%E7%94%A8&action=history" title="このページの過去の版 [h]" accesskey="h"><span>履歴表示</span></a></li> </ul> </div> </div> </nav> <nav class="vector-page-tools-landmark" aria-label="ページツール"> <div id="vector-page-tools-dropdown" class="vector-dropdown vector-page-tools-dropdown" > <input type="checkbox" id="vector-page-tools-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-tools-dropdown" class="vector-dropdown-checkbox " aria-label="ツール" > <label id="vector-page-tools-dropdown-label" for="vector-page-tools-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" ><span class="vector-dropdown-label-text">ツール</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-tools-unpinned-container" class="vector-unpinned-container"> <div id="vector-page-tools" class="vector-page-tools vector-pinnable-element"> <div class="vector-pinnable-header vector-page-tools-pinnable-header vector-pinnable-header-unpinned" data-feature-name="page-tools-pinned" data-pinnable-element-id="vector-page-tools" data-pinned-container-id="vector-page-tools-pinned-container" data-unpinned-container-id="vector-page-tools-unpinned-container" > <div class="vector-pinnable-header-label">ツール</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-page-tools.pin">サイドバーに移動</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-page-tools.unpin">非表示</button> </div> <div id="p-cactions" class="vector-menu mw-portlet mw-portlet-cactions emptyPortlet vector-has-collapsible-items" title="その他の操作" > <div class="vector-menu-heading"> 操作 </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-more-view" class="selected vector-more-collapsible-item mw-list-item"><a href="/wiki/%E3%82%B9%E3%83%94%E3%83%B3%E8%BB%8C%E9%81%93%E7%9B%B8%E4%BA%92%E4%BD%9C%E7%94%A8"><span>閲覧</span></a></li><li id="ca-more-edit" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=%E3%82%B9%E3%83%94%E3%83%B3%E8%BB%8C%E9%81%93%E7%9B%B8%E4%BA%92%E4%BD%9C%E7%94%A8&action=edit" title="このページのソースコードを編集する [e]" accesskey="e"><span>編集</span></a></li><li id="ca-more-history" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=%E3%82%B9%E3%83%94%E3%83%B3%E8%BB%8C%E9%81%93%E7%9B%B8%E4%BA%92%E4%BD%9C%E7%94%A8&action=history"><span>履歴表示</span></a></li> </ul> </div> </div> <div id="p-tb" class="vector-menu mw-portlet mw-portlet-tb" > <div class="vector-menu-heading"> 全般 </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="t-whatlinkshere" class="mw-list-item"><a href="/wiki/%E7%89%B9%E5%88%A5:%E3%83%AA%E3%83%B3%E3%82%AF%E5%85%83/%E3%82%B9%E3%83%94%E3%83%B3%E8%BB%8C%E9%81%93%E7%9B%B8%E4%BA%92%E4%BD%9C%E7%94%A8" title="ここにリンクしている全ウィキページの一覧 [j]" accesskey="j"><span>リンク元</span></a></li><li id="t-recentchangeslinked" class="mw-list-item"><a href="/wiki/%E7%89%B9%E5%88%A5:%E9%96%A2%E9%80%A3%E3%83%9A%E3%83%BC%E3%82%B8%E3%81%AE%E6%9B%B4%E6%96%B0%E7%8A%B6%E6%B3%81/%E3%82%B9%E3%83%94%E3%83%B3%E8%BB%8C%E9%81%93%E7%9B%B8%E4%BA%92%E4%BD%9C%E7%94%A8" rel="nofollow" title="このページからリンクしているページの最近の更新 [k]" accesskey="k"><span>関連ページの更新状況</span></a></li><li id="t-upload" class="mw-list-item"><a href="/wiki/Wikipedia:%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB%E3%81%AE%E3%82%A2%E3%83%83%E3%83%97%E3%83%AD%E3%83%BC%E3%83%89" title="ファイルをアップロードする [u]" accesskey="u"><span>ファイルをアップロード</span></a></li><li id="t-specialpages" class="mw-list-item"><a href="/wiki/%E7%89%B9%E5%88%A5:%E7%89%B9%E5%88%A5%E3%83%9A%E3%83%BC%E3%82%B8%E4%B8%80%E8%A6%A7" title="特別ページの一覧 [q]" accesskey="q"><span>特別ページ</span></a></li><li id="t-permalink" class="mw-list-item"><a href="/w/index.php?title=%E3%82%B9%E3%83%94%E3%83%B3%E8%BB%8C%E9%81%93%E7%9B%B8%E4%BA%92%E4%BD%9C%E7%94%A8&oldid=97300139" title="このページのこの版への固定リンク"><span>この版への固定リンク</span></a></li><li id="t-info" class="mw-list-item"><a href="/w/index.php?title=%E3%82%B9%E3%83%94%E3%83%B3%E8%BB%8C%E9%81%93%E7%9B%B8%E4%BA%92%E4%BD%9C%E7%94%A8&action=info" title="このページについての詳細情報"><span>ページ情報</span></a></li><li id="t-cite" class="mw-list-item"><a href="/w/index.php?title=%E7%89%B9%E5%88%A5:%E3%81%93%E3%81%AE%E3%83%9A%E3%83%BC%E3%82%B8%E3%82%92%E5%BC%95%E7%94%A8&page=%E3%82%B9%E3%83%94%E3%83%B3%E8%BB%8C%E9%81%93%E7%9B%B8%E4%BA%92%E4%BD%9C%E7%94%A8&id=97300139&wpFormIdentifier=titleform" title="このページの引用方法"><span>このページを引用</span></a></li><li id="t-urlshortener" class="mw-list-item"><a href="/w/index.php?title=%E7%89%B9%E5%88%A5:UrlShortener&url=https%3A%2F%2Fja.wikipedia.org%2Fwiki%2F%25E3%2582%25B9%25E3%2583%2594%25E3%2583%25B3%25E8%25BB%258C%25E9%2581%2593%25E7%259B%25B8%25E4%25BA%2592%25E4%25BD%259C%25E7%2594%25A8"><span>短縮URLを取得する</span></a></li><li id="t-urlshortener-qrcode" class="mw-list-item"><a href="/w/index.php?title=%E7%89%B9%E5%88%A5:QrCode&url=https%3A%2F%2Fja.wikipedia.org%2Fwiki%2F%25E3%2582%25B9%25E3%2583%2594%25E3%2583%25B3%25E8%25BB%258C%25E9%2581%2593%25E7%259B%25B8%25E4%25BA%2592%25E4%25BD%259C%25E7%2594%25A8"><span>QRコードをダウンロード</span></a></li> </ul> </div> </div> <div id="p-coll-print_export" class="vector-menu mw-portlet mw-portlet-coll-print_export" > <div class="vector-menu-heading"> 印刷/書き出し </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="coll-create_a_book" class="mw-list-item"><a href="/w/index.php?title=%E7%89%B9%E5%88%A5:%E3%83%96%E3%83%83%E3%82%AF&bookcmd=book_creator&referer=%E3%82%B9%E3%83%94%E3%83%B3%E8%BB%8C%E9%81%93%E7%9B%B8%E4%BA%92%E4%BD%9C%E7%94%A8"><span>ブックの新規作成</span></a></li><li id="coll-download-as-rl" class="mw-list-item"><a href="/w/index.php?title=%E7%89%B9%E5%88%A5:DownloadAsPdf&page=%E3%82%B9%E3%83%94%E3%83%B3%E8%BB%8C%E9%81%93%E7%9B%B8%E4%BA%92%E4%BD%9C%E7%94%A8&action=show-download-screen"><span>PDF 形式でダウンロード</span></a></li><li id="t-print" class="mw-list-item"><a href="/w/index.php?title=%E3%82%B9%E3%83%94%E3%83%B3%E8%BB%8C%E9%81%93%E7%9B%B8%E4%BA%92%E4%BD%9C%E7%94%A8&printable=yes" title="このページの印刷用ページ [p]" accesskey="p"><span>印刷用バージョン</span></a></li> </ul> </div> </div> <div id="p-wikibase-otherprojects" class="vector-menu mw-portlet mw-portlet-wikibase-otherprojects" > <div class="vector-menu-heading"> 他のプロジェクト </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="t-wikibase" class="wb-otherproject-link wb-otherproject-wikibase-dataitem mw-list-item"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q1570979" title="関連付けられたデータリポジトリ項目へのリンク [g]" accesskey="g"><span>ウィキデータ項目</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> </div> </div> </div> <div class="vector-column-end"> <div class="vector-sticky-pinned-container"> <nav class="vector-page-tools-landmark" aria-label="ページツール"> <div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="表示"> <div id="vector-appearance-pinned-container" class="vector-pinned-container"> <div id="vector-appearance" class="vector-appearance vector-pinnable-element"> <div class="vector-pinnable-header vector-appearance-pinnable-header vector-pinnable-header-pinned" data-feature-name="appearance-pinned" data-pinnable-element-id="vector-appearance" data-pinned-container-id="vector-appearance-pinned-container" data-unpinned-container-id="vector-appearance-unpinned-container" > <div class="vector-pinnable-header-label">表示</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">サイドバーに移動</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">非表示</button> </div> </div> </div> </nav> </div> </div> <div id="bodyContent" class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">出典: フリー百科事典『ウィキペディア（Wikipedia）』</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="ja" dir="ltr"><style data-mw-deduplicate="TemplateStyles:r101304250">.mw-parser-output .ambox{border:1px solid #a2a9b1;border-left:10px solid #36c;background-color:#fbfbfb;box-sizing:border-box}.mw-parser-output .ambox+link+.ambox,.mw-parser-output .ambox+link+style+.ambox,.mw-parser-output .ambox+link+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+style+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+link+.ambox{margin-top:-1px}html body.mediawiki .mw-parser-output .ambox.mbox-small-left{margin:4px 1em 4px 0;overflow:hidden;width:238px;border-collapse:collapse;font-size:88%;line-height:1.25em}.mw-parser-output .ambox-speedy{border-left:10px solid #b32424;background-color:#fee7e6}.mw-parser-output .ambox-delete{border-left:10px solid #b32424}.mw-parser-output .ambox-content{border-left:10px solid #f28500}.mw-parser-output .ambox-style{border-left:10px solid #fc3}.mw-parser-output .ambox-move{border-left:10px solid #9932cc}.mw-parser-output .ambox-protection{border-left:10px solid #a2a9b1}.mw-parser-output .ambox .mbox-text{border:none;padding:0.25em 0.5em;width:100%;font-size:90%}.mw-parser-output .ambox .mbox-image{border:none;padding:2px 0 2px 0.5em;text-align:center}.mw-parser-output .ambox .mbox-imageright{border:none;padding:2px 0.5em 2px 0;text-align:center}.mw-parser-output .ambox .mbox-empty-cell{border:none;padding:0;width:1px}.mw-parser-output .ambox .mbox-image-div{width:52px}html.client-js body.skin-minerva .mw-parser-output .mbox-text-span{margin-left:23px!important}@media(min-width:720px){.mw-parser-output .ambox{margin:0 10%}}@media print{body.ns-0 .mw-parser-output .ambox{display:none!important}}</style><table class="box-出典の明記 plainlinks metadata ambox ambox-content ambox-出典の明記" role="presentation"><tbody><tr><td class="mbox-image"><div class="mbox-image-div"><span typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/64/Question_book-4.svg/50px-Question_book-4.svg.png" decoding="async" width="50" height="39" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/64/Question_book-4.svg/75px-Question_book-4.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/64/Question_book-4.svg/100px-Question_book-4.svg.png 2x" data-file-width="262" data-file-height="204" /></span></span></div></td><td class="mbox-text"><div class="mbox-text-span"><b>この記事は<a href="/wiki/Wikipedia:%E6%A4%9C%E8%A8%BC%E5%8F%AF%E8%83%BD%E6%80%A7" title="Wikipedia:検証可能性">検証可能</a>な<a href="/wiki/Wikipedia:%E4%BF%A1%E9%A0%BC%E3%81%A7%E3%81%8D%E3%82%8B%E6%83%85%E5%A0%B1%E6%BA%90" title="Wikipedia:信頼できる情報源">参考文献や出典</a>が全く示されていないか、不十分です。</b><span class="hide-when-compact"> <a href="/wiki/Wikipedia:%E5%87%BA%E5%85%B8%E3%82%92%E6%98%8E%E8%A8%98%E3%81%99%E3%82%8B" title="Wikipedia:出典を明記する">出典を追加</a>して記事の信頼性向上にご協力ください。<small>（<a href="/wiki/Template:%E5%87%BA%E5%85%B8%E3%81%AE%E6%98%8E%E8%A8%98/doc" title="Template:出典の明記/doc">このテンプレートの使い方</a>）</small><br /><small><span class="plainlinks">出典検索<a href="/wiki/Template:Find_sources_mainspace" title="Template:Find sources mainspace"><sup>?</sup></a>: <a rel="nofollow" class="external text" href="//www.google.co.jp/search?hl=ja&as_eq=wikipedia&q=%22%E3%82%B9%E3%83%94%E3%83%B3%E8%BB%8C%E9%81%93%E7%9B%B8%E4%BA%92%E4%BD%9C%E7%94%A8%22&num=50">"スピン軌道相互作用"</a> – <a rel="nofollow" class="external text" href="//www.google.co.jp/search?hl=ja&q=%22%E3%82%B9%E3%83%94%E3%83%B3%E8%BB%8C%E9%81%93%E7%9B%B8%E4%BA%92%E4%BD%9C%E7%94%A8%22&tbm=nws">ニュース</a> <b>·</b> <a rel="nofollow" class="external text" href="//www.google.co.jp/search?hl=ja&tbs=bks:1&q=%22%E3%82%B9%E3%83%94%E3%83%B3%E8%BB%8C%E9%81%93%E7%9B%B8%E4%BA%92%E4%BD%9C%E7%94%A8%22">書籍</a> <b>·</b> <a rel="nofollow" class="external text" href="//scholar.google.co.jp/scholar?num=100&hl=ja&q=%22%E3%82%B9%E3%83%94%E3%83%B3%E8%BB%8C%E9%81%93%E7%9B%B8%E4%BA%92%E4%BD%9C%E7%94%A8%22">スカラー</a> <b>·</b> <a rel="nofollow" class="external text" href="https://ci.nii.ac.jp/opensearch/search?lang=ja&q=%22%E3%82%B9%E3%83%94%E3%83%B3%E8%BB%8C%E9%81%93%E7%9B%B8%E4%BA%92%E4%BD%9C%E7%94%A8%22&range=2&count=200&sortorder=1&type=0">CiNii</a> <b>·</b> <a rel="nofollow" class="external text" href="https://www.jstage.jst.go.jp/result/global/-char/ja?globalSearchKey=%22%E3%82%B9%E3%83%94%E3%83%B3%E8%BB%8C%E9%81%93%E7%9B%B8%E4%BA%92%E4%BD%9C%E7%94%A8%22">J-STAGE</a> <b>·</b> <a rel="nofollow" class="external text" href="https://ndlsearch.ndl.go.jp/api/openurl?any=%22%E3%82%B9%E3%83%94%E3%83%B3%E8%BB%8C%E9%81%93%E7%9B%B8%E4%BA%92%E4%BD%9C%E7%94%A8%22">NDL</a> <b>·</b> <a rel="nofollow" class="external text" href="https://dlib.jp/?q=%22%E3%82%B9%E3%83%94%E3%83%B3%E8%BB%8C%E9%81%93%E7%9B%B8%E4%BA%92%E4%BD%9C%E7%94%A8%22">dlib.jp</a> <b>·</b> <a rel="nofollow" class="external text" href="https://jpsearch.go.jp/csearch/jps-cross?csid=jps-cross&keyword=%22%E3%82%B9%E3%83%94%E3%83%B3%E8%BB%8C%E9%81%93%E7%9B%B8%E4%BA%92%E4%BD%9C%E7%94%A8%22">ジャパンサーチ</a> <b>·</b> <a rel="nofollow" class="external text" href="https://wikipedialibrary.wmflabs.org/partners/">TWL</a></span></small></span> <span class="date-container"><i>(<span class="date"><span title="2023-01">2023年1月</span></span>)</i></span></div></td></tr></tbody></table> <p><b>スピン軌道相互作用</b>（<a href="/wiki/%E8%8B%B1%E8%AA%9E" title="英語">英</a>: <span lang="en">Spin orbit coupling</span>、稀に<a href="/wiki/%E8%8B%B1%E8%AA%9E" title="英語">英</a>: <span lang="en">Spin orbit interaction</span>）とは<a href="/wiki/%E9%9B%BB%E5%AD%90" title="電子">電子</a>の<a href="/wiki/%E3%82%B9%E3%83%94%E3%83%B3%E8%A7%92%E9%81%8B%E5%8B%95%E9%87%8F" title="スピン角運動量">スピン</a>と、電子の<a href="/wiki/%E8%BB%8C%E9%81%93%E8%A7%92%E9%81%8B%E5%8B%95%E9%87%8F" title="軌道角運動量">軌道角運動量</a>との相互作用のこと。 </p><p>相対論的に取り扱われる<a href="/wiki/%E3%83%87%E3%82%A3%E3%83%A9%E3%83%83%E3%82%AF%E6%96%B9%E7%A8%8B%E5%BC%8F" title="ディラック方程式">ディラック方程式</a>（<a href="/wiki/%E7%9B%B8%E5%AF%BE%E8%AB%96%E7%9A%84%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6" title="相対論的量子力学">相対論的量子力学</a>）では自然に導入される概念である。スピン軌道相互作用により、<a href="/wiki/%E7%B8%AE%E9%80%80" title="縮退">縮退</a>していた電子の<a href="/wiki/%E3%82%A8%E3%83%8D%E3%83%AB%E3%82%AE%E3%83%BC%E5%9B%BA%E6%9C%89%E5%80%A4" class="mw-redirect" title="エネルギー固有値">エネルギー固有値</a>が分裂する。 </p><p><a href="/wiki/%E3%83%9E%E3%83%AA%E3%82%A2%E3%83%BB%E3%82%B2%E3%83%83%E3%83%91%E3%83%BC%E3%83%88%EF%BC%9D%E3%83%A1%E3%82%A4%E3%83%A4%E3%83%BC" title="マリア・ゲッパート＝メイヤー">ゲッパート＝マイヤー</a>と<a href="/wiki/%E3%83%A8%E3%83%8F%E3%83%8D%E3%82%B9%E3%83%BB%E3%83%8F%E3%83%B3%E3%82%B9%E3%83%BB%E3%82%A4%E3%82%A7%E3%83%B3%E3%82%BC%E3%83%B3" title="ヨハネス・ハンス・イェンゼン">イェンセン</a>は、原子核の問題について、スピン軌道相互作用を導入した<a href="/wiki/%E6%AE%BB%E6%A8%A1%E5%9E%8B" title="殻模型">殻模型</a>を用いれば、その準位の分裂から、実験的に知られていた安定な核子数、<a href="/wiki/%E9%AD%94%E6%B3%95%E6%95%B0" title="魔法数">魔法数</a>を説明できることを発見し、<a href="/wiki/%E3%83%8E%E3%83%BC%E3%83%99%E3%83%AB%E8%B3%9E" title="ノーベル賞">ノーベル賞</a>を受賞した。 </p><p>原子の<a href="/wiki/%E6%9C%80%E5%A4%96%E6%AE%BB%E9%9B%BB%E5%AD%90" class="mw-redirect" title="最外殻電子">最外殻電子</a>ではスピン軌道相互作用によりスピン・軌道角運動量の向きがそろうことがある。常温の範囲では分裂した準位（LS多重項という）の中で最低エネルギーをもつ準位に状態がある確率が高い。最低エネルギーの多重項を知るために<a href="/wiki/%E3%83%95%E3%83%B3%E3%83%88%E3%81%AE%E8%A6%8F%E5%89%87" title="フントの規則">フントの規則</a>とよばれる実験則が有効である。 </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="古典的な説明"><span id=".E5.8F.A4.E5.85.B8.E7.9A.84.E3.81.AA.E8.AA.AC.E6.98.8E"></span>古典的な説明</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E3%82%B9%E3%83%94%E3%83%B3%E8%BB%8C%E9%81%93%E7%9B%B8%E4%BA%92%E4%BD%9C%E7%94%A8&action=edit&section=1" title="節を編集: 古典的な説明"><span>編集</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r101304250"><table class="box-出典の明記 plainlinks metadata ambox mbox-small-left ambox-content ambox-出典の明記" role="presentation" style="width:auto;"><tbody><tr><td class="mbox-image"><span typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/64/Question_book-4.svg/50px-Question_book-4.svg.png" decoding="async" width="50" height="39" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/64/Question_book-4.svg/75px-Question_book-4.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/64/Question_book-4.svg/100px-Question_book-4.svg.png 2x" data-file-width="262" data-file-height="204" /></span></span></td><td class="mbox-text"><div class="mbox-text-span"><b>この節は<a href="/wiki/Wikipedia:%E6%A4%9C%E8%A8%BC%E5%8F%AF%E8%83%BD%E6%80%A7" title="Wikipedia:検証可能性">検証可能</a>な<a href="/wiki/Wikipedia:%E4%BF%A1%E9%A0%BC%E3%81%A7%E3%81%8D%E3%82%8B%E6%83%85%E5%A0%B1%E6%BA%90" title="Wikipedia:信頼できる情報源">参考文献や出典</a>が全く示されていないか、不十分です。</b><span class="hide-when-compact"> <a href="/wiki/Wikipedia:%E5%87%BA%E5%85%B8%E3%82%92%E6%98%8E%E8%A8%98%E3%81%99%E3%82%8B" title="Wikipedia:出典を明記する">出典を追加</a>して記事の信頼性向上にご協力ください。<small>（<a href="/wiki/Template:%E5%87%BA%E5%85%B8%E3%81%AE%E6%98%8E%E8%A8%98/doc" title="Template:出典の明記/doc">このテンプレートの使い方</a>）</small><br /><small><span class="plainlinks">出典検索<a href="/wiki/Template:Find_sources_mainspace" title="Template:Find sources mainspace"><sup>?</sup></a>: <a rel="nofollow" class="external text" href="//www.google.co.jp/search?hl=ja&as_eq=wikipedia&q=%22%E3%82%B9%E3%83%94%E3%83%B3%E8%BB%8C%E9%81%93%E7%9B%B8%E4%BA%92%E4%BD%9C%E7%94%A8%22&num=50">"スピン軌道相互作用"</a> – <a rel="nofollow" class="external text" href="//www.google.co.jp/search?hl=ja&q=%22%E3%82%B9%E3%83%94%E3%83%B3%E8%BB%8C%E9%81%93%E7%9B%B8%E4%BA%92%E4%BD%9C%E7%94%A8%22&tbm=nws">ニュース</a> <b>·</b> <a rel="nofollow" class="external text" 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href="https://ndlsearch.ndl.go.jp/api/openurl?any=%22%E3%82%B9%E3%83%94%E3%83%B3%E8%BB%8C%E9%81%93%E7%9B%B8%E4%BA%92%E4%BD%9C%E7%94%A8%22">NDL</a> <b>·</b> <a rel="nofollow" class="external text" href="https://dlib.jp/?q=%22%E3%82%B9%E3%83%94%E3%83%B3%E8%BB%8C%E9%81%93%E7%9B%B8%E4%BA%92%E4%BD%9C%E7%94%A8%22">dlib.jp</a> <b>·</b> <a rel="nofollow" class="external text" href="https://jpsearch.go.jp/csearch/jps-cross?csid=jps-cross&keyword=%22%E3%82%B9%E3%83%94%E3%83%B3%E8%BB%8C%E9%81%93%E7%9B%B8%E4%BA%92%E4%BD%9C%E7%94%A8%22">ジャパンサーチ</a> <b>·</b> <a rel="nofollow" class="external text" href="https://wikipedialibrary.wmflabs.org/partners/">TWL</a></span></small></span> <span class="date-container"><i>(<span class="date"><span title="2023-01">2023年1月</span></span>)</i></span></div></td></tr></tbody></table> <p>水素原子内の電子は陽子のまわりを回転しているが、これを電子の上に乗っている人から見ると、電子のまわりを陽子が回転しているように見える。回転している陽子は円形電流とみなすことができ、<a href="/wiki/%E3%83%93%E3%82%AA%E3%83%BB%E3%82%B5%E3%83%90%E3%83%BC%E3%83%AB%E3%81%AE%E6%B3%95%E5%89%87" title="ビオ・サバールの法則">ビオ・サバールの法則</a>により、それは電子上に磁場<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {B} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">B</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {B} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cafb0ef39b0f5ffa23c170aa7f7b4e718327c4d1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.901ex; height:2.176ex;" alt="{\displaystyle \mathbf {B} }"></span>を作る。その磁場が電子のスピンによる磁気双極子モーメント<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {\mu } }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {\mu } }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e407f1e8e83fffbed7e61f4112b7eef6b22b9e67" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.402ex; height:2.176ex;" alt="{\displaystyle \mathbf {\mu } }"></span>に作用する。この相互作用は<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {B} \cdot \mathbf {\mu } }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">B</mi> </mrow> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {B} \cdot \mathbf {\mu } }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/343e48a6da1117dfb387fbed5f6b05a6419cbf92" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.982ex; height:2.676ex;" alt="{\displaystyle \mathbf {B} \cdot \mathbf {\mu } }"></span>に比例する。<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {\mu } }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {\mu } }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e407f1e8e83fffbed7e61f4112b7eef6b22b9e67" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.402ex; height:2.176ex;" alt="{\displaystyle \mathbf {\mu } }"></span>はスピン角運動量<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {s} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">s</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {s} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/644ae690160e658898a141e568a7fb0ee6040004" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.056ex; height:1.676ex;" alt="{\displaystyle \mathbf {s} }"></span>に比例している。一方で陽子のつくる磁場<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {B} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">B</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {B} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cafb0ef39b0f5ffa23c170aa7f7b4e718327c4d1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.901ex; height:2.176ex;" alt="{\displaystyle \mathbf {B} }"></span>は陽子の磁気双極子モーメント<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {\mu ^{(P)}} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <msup> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo mathvariant="bold" stretchy="false">(</mo> <mi mathvariant="bold">P</mi> <mo mathvariant="bold" stretchy="false">)</mo> </mrow> </msup> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {\mu ^{(P)}} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3126360a2371e5880f645d6312a322a1390317c1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.395ex; height:3.343ex;" alt="{\displaystyle \mathbf {\mu ^{(P)}} }"></span>に比例し、その<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {\mu ^{(P)}} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <msup> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo mathvariant="bold" stretchy="false">(</mo> <mi mathvariant="bold">P</mi> <mo mathvariant="bold" stretchy="false">)</mo> </mrow> </msup> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {\mu ^{(P)}} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3126360a2371e5880f645d6312a322a1390317c1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.395ex; height:3.343ex;" alt="{\displaystyle \mathbf {\mu ^{(P)}} }"></span>は陽子の軌道角運動量<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {L} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">L</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {L} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6f5f750865376a1a4ae2b15a00b4ff9c75a66630" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.608ex; height:2.176ex;" alt="{\displaystyle \mathbf {L} }"></span>に比例している。したがってこの場合の電子-陽子間の相互作用エネルギーは<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {s\cdot L} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">s</mi> <mo>⋅</mo> <mi mathvariant="bold">L</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {s\cdot L} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d416c5e5fea5f5d222c3f548393d4fe756c14c32" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:4.343ex; height:2.176ex;" alt="{\displaystyle \mathbf {s\cdot L} }"></span>に比例する<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup>。 </p> <div class="mw-heading mw-heading2"><h2 id="具体的な表式"><span id=".E5.85.B7.E4.BD.93.E7.9A.84.E3.81.AA.E8.A1.A8.E5.BC.8F"></span>具体的な表式</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E3%82%B9%E3%83%94%E3%83%B3%E8%BB%8C%E9%81%93%E7%9B%B8%E4%BA%92%E4%BD%9C%E7%94%A8&action=edit&section=2" title="節を編集: 具体的な表式"><span>編集</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r101304250"><table class="box-出典の明記 plainlinks metadata ambox mbox-small-left ambox-content ambox-出典の明記" role="presentation" style="width:auto;"><tbody><tr><td class="mbox-image"><span typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/64/Question_book-4.svg/50px-Question_book-4.svg.png" decoding="async" width="50" height="39" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/64/Question_book-4.svg/75px-Question_book-4.svg.png 1.5x, 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title="2023-01">2023年1月</span></span>)</i></span></div></td></tr></tbody></table> <p>球対称な<a href="/wiki/%E3%83%9D%E3%83%86%E3%83%B3%E3%82%B7%E3%83%A3%E3%83%AB" title="ポテンシャル">ポテンシャル</a>中での一電子に関する、スピン軌道相互作用 <i>H</i><sub>SO</sub> は、 </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle H_{\rm {SO}}=V(r)(\mathbf {l} \cdot \mathbf {s} )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>H</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">S</mi> <mi mathvariant="normal">O</mi> </mrow> </mrow> </msub> <mo>=</mo> <mi>V</mi> <mo stretchy="false">(</mo> <mi>r</mi> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">l</mi> </mrow> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">s</mi> </mrow> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle H_{\rm {SO}}=V(r)(\mathbf {l} \cdot \mathbf {s} )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/06da0492722aeec87eae86f03b65fd330e25d34e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:17.386ex; height:2.843ex;" alt="{\displaystyle H_{\rm {SO}}=V(r)(\mathbf {l} \cdot \mathbf {s} )}"></span></dd></dl> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V(r)=-(g-1)\left({e\hbar ^{2} \over {2m^{2}c^{2}}}\right)\left({1 \over r}{d\phi (r) \over {dr}}\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>V</mi> <mo stretchy="false">(</mo> <mi>r</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mo>−</mo> <mo stretchy="false">(</mo> <mi>g</mi> <mo>−</mo> <mn>1</mn> <mo stretchy="false">)</mo> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>e</mi> <msup> <mi class="MJX-variant">ℏ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> <msup> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mi>r</mi> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>d</mi> <mi>ϕ</mi> <mo stretchy="false">(</mo> <mi>r</mi> <mo stretchy="false">)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>d</mi> <mi>r</mi> </mrow> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V(r)=-(g-1)\left({e\hbar ^{2} \over {2m^{2}c^{2}}}\right)\left({1 \over r}{d\phi (r) \over {dr}}\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e30c272ac7f3e219d1350bfeadae6368d2dee9f1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:39.545ex; height:6.343ex;" alt="{\displaystyle V(r)=-(g-1)\left({e\hbar ^{2} \over {2m^{2}c^{2}}}\right)\left({1 \over r}{d\phi (r) \over {dr}}\right)}"></span></dd></dl> <p><b>l</b> は<a href="/wiki/%E8%BB%8C%E9%81%93%E8%A7%92%E9%81%8B%E5%8B%95%E9%87%8F" title="軌道角運動量">軌道角運動量</a>、<b>s</b> は<a href="/wiki/%E3%82%B9%E3%83%94%E3%83%B3%E8%A7%92%E9%81%8B%E5%8B%95%E9%87%8F" title="スピン角運動量">スピン角運動量</a>（共に、<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \hbar }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi class="MJX-variant">ℏ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \hbar }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/de68de3a92517953436c93b5a76461d49160cc41" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.306ex; height:2.176ex;" alt="{\displaystyle \hbar }"></span> を単位とする）、<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \hbar =h/2\pi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi class="MJX-variant">ℏ</mi> <mo>=</mo> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> <mi>π</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \hbar =h/2\pi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f836f3a2de168369eb9f80f4057518222ecde88b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:9.401ex; height:2.843ex;" alt="{\displaystyle \hbar =h/2\pi }"></span> で、<i>h</i> は<a href="/wiki/%E3%83%97%E3%83%A9%E3%83%B3%E3%82%AF%E5%AE%9A%E6%95%B0" title="プランク定数">プランク定数</a>、<i>e</i> は<a href="/wiki/%E7%B4%A0%E9%9B%BB%E8%8D%B7" class="mw-redirect" title="素電荷">素電荷</a>、<i>m</i> は電子の質量、<i>r</i> は電子の位置座標、<i>c</i> は<a href="/wiki/%E5%85%89%E9%80%9F" title="光速">光速</a>、<i>g</i> は <a href="/wiki/G%E5%9B%A0%E5%AD%90" title="G因子"><i>g</i>因子</a>（真空中の<a href="/wiki/%E8%87%AA%E7%94%B1%E9%9B%BB%E5%AD%90" title="自由電子">自由電子</a>の場合、<i>g</i> = 2）である。φ は球対称場での<a href="/wiki/%E9%9B%BB%E5%A0%B4" title="電場">電場</a>（<b>E</b>(<i>r</i>) とする）に対する<a href="/wiki/%E3%82%B9%E3%82%AB%E3%83%A9%E3%83%BC%E3%83%9D%E3%83%86%E3%83%B3%E3%82%B7%E3%83%A3%E3%83%AB" title="スカラーポテンシャル">スカラーポテンシャル</a>で、 </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {E} (r)=-\mathrm {grad} \,\phi (r)=-\mathbf {r} \left({1 \over r}{d\phi (r) \over {dr}}\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">E</mi> </mrow> <mo stretchy="false">(</mo> <mi>r</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">g</mi> <mi mathvariant="normal">r</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">d</mi> </mrow> <mspace width="thinmathspace" /> <mi>ϕ</mi> <mo stretchy="false">(</mo> <mi>r</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mrow> <mo>(</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mi>r</mi> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>d</mi> <mi>ϕ</mi> <mo stretchy="false">(</mo> <mi>r</mi> <mo stretchy="false">)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>d</mi> <mi>r</mi> </mrow> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {E} (r)=-\mathrm {grad} \,\phi (r)=-\mathbf {r} \left({1 \over r}{d\phi (r) \over {dr}}\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/28855c6284ba304ddb47e6c89d9bced880a3e851" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:36.792ex; height:6.343ex;" alt="{\displaystyle \mathbf {E} (r)=-\mathrm {grad} \,\phi (r)=-\mathbf {r} \left({1 \over r}{d\phi (r) \over {dr}}\right)}"></span></dd></dl> <p>である。 </p><p>ポテンシャルが非球対称の場合は、 </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle H_{\rm {SO}}=(g-1)\left({e\hbar \over {2mc^{2}}}\right)[E(\mathbf {r} )\times \mathbf {v} ]\cdot \mathbf {s} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>H</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">S</mi> <mi mathvariant="normal">O</mi> </mrow> </mrow> </msub> <mo>=</mo> <mo stretchy="false">(</mo> <mi>g</mi> <mo>−</mo> <mn>1</mn> <mo stretchy="false">)</mo> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>e</mi> <mi class="MJX-variant">ℏ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> <mi>m</mi> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mo stretchy="false">[</mo> <mi>E</mi> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mo stretchy="false">)</mo> <mo>×</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">v</mi> </mrow> <mo stretchy="false">]</mo> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">s</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle H_{\rm {SO}}=(g-1)\left({e\hbar \over {2mc^{2}}}\right)[E(\mathbf {r} )\times \mathbf {v} ]\cdot \mathbf {s} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6eacea125e0d584489cbff43ccc1be97f24c002d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:37.645ex; height:6.176ex;" alt="{\displaystyle H_{\rm {SO}}=(g-1)\left({e\hbar \over {2mc^{2}}}\right)[E(\mathbf {r} )\times \mathbf {v} ]\cdot \mathbf {s} }"></span></dd></dl> <p>となる。<b>v</b> は電子の速度、<i>E</i>(<b>r</b>) は球対称でない<a href="/wiki/%E9%9B%BB%E5%A0%B4" title="電場">電場</a>。 </p><p>非相対論的な<a href="/wiki/%E3%82%B7%E3%83%A5%E3%83%AC%E3%83%BC%E3%83%87%E3%82%A3%E3%83%B3%E3%82%AC%E3%83%BC%E6%96%B9%E7%A8%8B%E5%BC%8F" title="シュレーディンガー方程式">シュレーディンガー方程式</a>に対し、最も影響の大きい<a href="/wiki/%E7%9B%B8%E5%AF%BE%E8%AB%96%E5%8A%B9%E6%9E%9C" title="相対論効果">相対論効果</a>はスピン軌道相互作用の項なので、これを<a href="/wiki/%E6%91%82%E5%8B%95" title="摂動">摂動</a>項としてシュレーディンガー方程式に取り入れて解かれることがある。 </p><p>（補足）<br />上に挙げた電子以外に、<a href="/wiki/%E5%8E%9F%E5%AD%90%E6%A0%B8" title="原子核">原子核</a>の核子（<a href="/wiki/%E9%99%BD%E5%AD%90" title="陽子">陽子</a>や<a href="/wiki/%E4%B8%AD%E6%80%A7%E5%AD%90" title="中性子">中性子</a>）もスピンを持つので（核スピン）、これらに関してのスピン軌道相互作用が存在する。 </p> <div class="mw-heading mw-heading2"><h2 id="スピン軌道分裂"><span id=".E3.82.B9.E3.83.94.E3.83.B3.E8.BB.8C.E9.81.93.E5.88.86.E8.A3.82"></span>スピン軌道分裂</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E3%82%B9%E3%83%94%E3%83%B3%E8%BB%8C%E9%81%93%E7%9B%B8%E4%BA%92%E4%BD%9C%E7%94%A8&action=edit&section=3" title="節を編集: スピン軌道分裂"><span>編集</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r101304250"><table class="box-出典の明記 plainlinks metadata ambox mbox-small-left ambox-content ambox-出典の明記" role="presentation" style="width:auto;"><tbody><tr><td class="mbox-image"><span typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/64/Question_book-4.svg/50px-Question_book-4.svg.png" decoding="async" width="50" height="39" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/64/Question_book-4.svg/75px-Question_book-4.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/64/Question_book-4.svg/100px-Question_book-4.svg.png 2x" data-file-width="262" data-file-height="204" /></span></span></td><td class="mbox-text"><div 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title="2023-01">2023年1月</span></span>)</i></span></div></td></tr></tbody></table> <p>スピン軌道相互作用<i>H<sub>SO</sub></i> が一粒子ポテンシャルに付け加わる場合を摂動論で考える。 </p><p>一体ハミルトニアン<i>H<sub>0</sub></i> = <i>T</i> + <i>U(r)</i> の固有値問題を解くことによって一粒子準位<i>E<sub>nl</sub></i> と一粒子波動関数<i>R<sub>nl</sub></i>(<i>r</i>)<i>Y<sub>lm</sub></i>(<i>θ,φ</i>)が求められているとする。粒子のスピンは1/2とする。 </p><p>このような相互作用があると、スピン角運動量<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {s} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">s</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {s} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/644ae690160e658898a141e568a7fb0ee6040004" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.056ex; height:1.676ex;" alt="{\displaystyle \mathbf {s} }"></span>と軌道角運動量<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {l} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">l</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {l} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dca0b04733c4e44533df8a7eb12145d74cdbefef" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.742ex; height:2.176ex;" alt="{\displaystyle \mathbf {l} }"></span>は別々に<a href="/wiki/%E8%89%AF%E3%81%84%E9%87%8F%E5%AD%90%E6%95%B0" title="良い量子数">良い量子数</a>になることができなくなり、全角運動量のみが良い量子数になる。<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 j}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>j</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle j}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2f461e54f5c093e92a55547b9764291390f0b5d0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.027ex; width:0.985ex; height:2.509ex;" alt="{\displaystyle j}"></span>の値としては<a href="/wiki/%E8%A7%92%E9%81%8B%E5%8B%95%E9%87%8F%E3%81%AE%E5%90%88%E6%88%90" title="角運動量の合成">角運動量の合成</a>則から<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 l+(1/2)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>l</mi> <mo>+</mo> <mo stretchy="false">(</mo> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle l+(1/2)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/59d5728fc64dabae56378328e07b1ce0cc23e17d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:8.83ex; height:2.843ex;" alt="{\displaystyle l+(1/2)}"></span>と<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 l-(1/2)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>l</mi> <mo>−</mo> <mo stretchy="false">(</mo> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle l-(1/2)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c5e55eaee7c1362bdc3ab92dbdafb56847538368" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:8.83ex; height:2.843ex;" alt="{\displaystyle l-(1/2)}"></span>が可能である。 </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {s\cdot l} =(1/2)(\mathbf {j} ^{2}-\mathbf {s} ^{2}-\mathbf {l} ^{2})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">s</mi> <mo>⋅</mo> <mi mathvariant="bold">l</mi> </mrow> <mo>=</mo> <mo stretchy="false">(</mo> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">j</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">s</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">l</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {s\cdot l} =(1/2)(\mathbf {j} ^{2}-\mathbf {s} ^{2}-\mathbf {l} ^{2})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fcc190339e0b1bd0c61fa0e20dbdaa2a58f7da18" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:25.139ex; height:3.176ex;" alt="{\displaystyle \mathbf {s\cdot l} =(1/2)(\mathbf {j} ^{2}-\mathbf {s} ^{2}-\mathbf {l} ^{2})}"></span></dd></dl> <p>であるから、<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {s\cdot l} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">s</mi> <mo>⋅</mo> <mi mathvariant="bold">l</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {s\cdot l} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/19060256f8fe0e7bf7ece04f2fa9e54e94ddf3b5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.477ex; height:2.176ex;" alt="{\displaystyle \mathbf {s\cdot l} }"></span>の期待値は<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 j=l+1/2}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>j</mi> <mo>=</mo> <mi>l</mi> <mo>+</mo> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle j=l+1/2}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/60b19816c790ec8588f8b609eaf496449fc08d5a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; margin-left: -0.027ex; width:11.104ex; height:2.843ex;" alt="{\displaystyle j=l+1/2}"></span>に対して<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 l/2}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>l</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle l/2}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87747c775608cb9e71f408b1453ee9df9f6e130b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:3.018ex; height:2.843ex;" alt="{\displaystyle l/2}"></span>、<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 j=l-1/2}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>j</mi> <mo>=</mo> <mi>l</mi> <mo>−</mo> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle j=l-1/2}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/95c0830f667b723e314b09b12faedbb004abd718" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; margin-left: -0.027ex; width:11.104ex; height:2.843ex;" alt="{\displaystyle j=l-1/2}"></span>に対して<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 -(l+1)/2}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>−</mo> <mo stretchy="false">(</mo> <mi>l</mi> <mo>+</mo> <mn>1</mn> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle -(l+1)/2}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/93157b4fccaa847c8a5a08bdd4defdfa829b313c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:10.638ex; height:2.843ex;" alt="{\displaystyle -(l+1)/2}"></span>と得られる。 </p><p>動径積分を<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 \xi _{nl}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ξ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mi>l</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \xi _{nl}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/23a09be3b89d15e72d586aaee7de5363309cfb24" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.727ex; height:2.509ex;" alt="{\displaystyle \xi _{nl}}"></span>とおくと、<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 j=l-1/2}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>j</mi> <mo>=</mo> <mi>l</mi> <mo>−</mo> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle j=l-1/2}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/95c0830f667b723e314b09b12faedbb004abd718" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; margin-left: -0.027ex; width:11.104ex; height:2.843ex;" alt="{\displaystyle j=l-1/2}"></span>の軌道と<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 j=l+1/2}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>j</mi> <mo>=</mo> <mi>l</mi> <mo>+</mo> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle j=l+1/2}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/60b19816c790ec8588f8b609eaf496449fc08d5a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; margin-left: -0.027ex; width:11.104ex; height:2.843ex;" alt="{\displaystyle j=l+1/2}"></span>の軌道のエネルギー差は<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 -\{l+(1/2)\}\xi _{nl}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>−</mo> <mo fence="false" stretchy="false">{</mo> <mi>l</mi> <mo>+</mo> <mo stretchy="false">(</mo> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> <mo stretchy="false">)</mo> <mo fence="false" stretchy="false">}</mo> <msub> <mi>ξ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mi>l</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle -\{l+(1/2)\}\xi _{nl}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/26d92bc047c80b138dd81f7ce2708a799b8a3fc4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:15.691ex; height:2.843ex;" alt="{\displaystyle -\{l+(1/2)\}\xi _{nl}}"></span>となる。また<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 \xi _{nl}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ξ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mi>l</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \xi _{nl}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/23a09be3b89d15e72d586aaee7de5363309cfb24" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.727ex; height:2.509ex;" alt="{\displaystyle \xi _{nl}}"></span>が<i>n</i> および<i>l</i> によって余り変化しないものとすれば、スピン軌道分裂は<i>l</i>の値が大きいほど大きくなる。 </p> <div class="mw-heading mw-heading2"><h2 id="関連項目"><span id=".E9.96.A2.E9.80.A3.E9.A0.85.E7.9B.AE"></span>関連項目</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E3%82%B9%E3%83%94%E3%83%B3%E8%BB%8C%E9%81%93%E7%9B%B8%E4%BA%92%E4%BD%9C%E7%94%A8&action=edit&section=4" title="節を編集: 関連項目"><span>編集</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6" title="量子力学">量子力学</a></li> <li><a href="/wiki/%E7%89%A9%E6%80%A7%E7%89%A9%E7%90%86%E5%AD%A6" title="物性物理学">物性物理学</a></li> <li><a href="/wiki/%E5%BE%AE%E7%B4%B0%E6%A7%8B%E9%80%A0_(%E5%8E%9F%E5%AD%90%E7%89%A9%E7%90%86%E5%AD%A6)" title="微細構造 (原子物理学)">微細構造</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="参考文献"><span id=".E5.8F.82.E8.80.83.E6.96.87.E7.8C.AE"></span>参考文献</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E3%82%B9%E3%83%94%E3%83%B3%E8%BB%8C%E9%81%93%E7%9B%B8%E4%BA%92%E4%BD%9C%E7%94%A8&action=edit&section=5" title="節を編集: 参考文献"><span>編集</span></a><span class="mw-editsection-bracket">]</span></span></div> <ol class="references"> <li id="cite_note-1"><b><a href="#cite_ref-1">^</a></b> <span class="reference-text"><cite style="font-style:normal" class="citation book">砂川重信『量子力学』<a href="/wiki/%E5%B2%A9%E6%B3%A2%E6%9B%B8%E5%BA%97" title="岩波書店">岩波書店</a>、1991年。<a href="/wiki/%E7%89%B9%E5%88%A5:%E6%96%87%E7%8C%AE%E8%B3%87%E6%96%99/4000061399" class="internal mw-magiclink-isbn">ISBN 4000061399</a>。</cite><span class="Z3988" 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