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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="https://donate.wikimedia.org/?wmf_source=donate&wmf_medium=sidebar&wmf_campaign=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%83%9D%E3%83%86%E3%83%B3%E3%82%B7%E3%83%A3%E3%83%AB" 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%83%9D%E3%83%86%E3%83%B3%E3%82%B7%E3%83%A3%E3%83%AB" 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-ポテンシャル（狭義）" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#ポテンシャル（狭義）"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>ポテンシャル（狭義）</span> </div> </a> <ul id="toc-ポテンシャル（狭義）-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-保存力" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#保存力"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>保存力</span> </div> </a> <ul id="toc-保存力-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-ベクトルポテンシャル" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#ベクトルポテンシャル"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>ベクトルポテンシャル</span> </div> </a> <ul id="toc-ベクトルポテンシャル-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-ポテンシャルエネルギー" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#ポテンシャルエネルギー"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>ポテンシャルエネルギー</span> </div> </a> <ul id="toc-ポテンシャルエネルギー-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> <li id="toc-関連記事" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#関連記事"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>関連記事</span> </div> </a> <button aria-controls="toc-関連記事-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>関連記事サブセクションを切り替えます</span> </button> <ul id="toc-関連記事-sublist" class="vector-toc-list"> <li id="toc-その他のポテンシャル" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#その他のポテンシャル"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.1</span> <span>その他のポテンシャル</span> </div> </a> <ul id="toc-その他のポテンシャル-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="目次" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" title="目次" > <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">ポテンシャル</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9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-9" 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">9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-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Potential_(Physik)" title="ドイツ語: Potential (Physik)" lang="de" hreflang="de" data-title="Potential (Physik)" 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-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Potencial_(f%C3%ADsica)" title="スペイン語: Potencial (física)" lang="es" hreflang="es" data-title="Potencial (física)" data-language-autonym="Español" data-language-local-name="スペイン語" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Potentsiaal" title="エストニア語: Potentsiaal" lang="et" hreflang="et" data-title="Potentsiaal" data-language-autonym="Eesti" data-language-local-name="エストニア語" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Razlika_potencijala" title="クロアチア語: Razlika potencijala" lang="hr" hreflang="hr" data-title="Razlika potencijala" data-language-autonym="Hrvatski" data-language-local-name="クロアチア語" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Potenziale" title="イタリア語: Potenziale" lang="it" hreflang="it" data-title="Potenziale" 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-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%9F%D0%BE%D1%82%D0%B5%D0%BD%D1%86%D0%B8%D0%B0%D0%BB" title="カザフ語: Потенциал" lang="kk" hreflang="kk" data-title="Потенциал" data-language-autonym="Қазақша" data-language-local-name="カザフ語" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Razlika_potencijala" title="セルボ・クロアチア語: Razlika potencijala" lang="sh" hreflang="sh" data-title="Razlika potencijala" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="セルボ・クロアチア語" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Potencial" title="スロベニア語: Potencial" lang="sl" hreflang="sl" data-title="Potencial" data-language-autonym="Slovenščina" data-language-local-name="スロベニア語" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Potential" title="スウェーデン語: Potential" lang="sv" hreflang="sv" data-title="Potential" data-language-autonym="Svenska" data-language-local-name="スウェーデン語" class="interlanguage-link-target"><span>Svenska</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/Q12559031#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%83%9D%E3%83%86%E3%83%B3%E3%82%B7%E3%83%A3%E3%83%AB" 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%83%9D%E3%83%86%E3%83%B3%E3%82%B7%E3%83%A3%E3%83%AB&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%83%9D%E3%83%86%E3%83%B3%E3%82%B7%E3%83%A3%E3%83%AB"><span>閲覧</span></a></li><li id="ca-edit" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=%E3%83%9D%E3%83%86%E3%83%B3%E3%82%B7%E3%83%A3%E3%83%AB&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%83%9D%E3%83%86%E3%83%B3%E3%82%B7%E3%83%A3%E3%83%AB&action=history" title="このページの過去の版[h]" accesskey="h"><span>履歴を表示</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%83%9D%E3%83%86%E3%83%B3%E3%82%B7%E3%83%A3%E3%83%AB"><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%83%9D%E3%83%86%E3%83%B3%E3%82%B7%E3%83%A3%E3%83%AB&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%83%9D%E3%83%86%E3%83%B3%E3%82%B7%E3%83%A3%E3%83%AB&action=history"><span>履歴を表示</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%83%9D%E3%83%86%E3%83%B3%E3%82%B7%E3%83%A3%E3%83%AB" 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%83%9D%E3%83%86%E3%83%B3%E3%82%B7%E3%83%A3%E3%83%AB" 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="//ja.wikipedia.org/wiki/Wikipedia:ファイルのアップロード" 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 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.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-単一の出典 plainlinks metadata ambox ambox-content" 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/a/a1/2017-fr.wp-orange-source.svg/45px-2017-fr.wp-orange-source.svg.png" decoding="async" width="45" height="45" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a1/2017-fr.wp-orange-source.svg/68px-2017-fr.wp-orange-source.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a1/2017-fr.wp-orange-source.svg/90px-2017-fr.wp-orange-source.svg.png 2x" data-file-width="512" data-file-height="512" /></span></span></div></td><td class="mbox-text"><div class="mbox-text-span"><b>この記事のほとんどまたは全てが<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">唯一の出典</a>にのみ基づいています</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">他の出典の追加</a>も行い、記事の正確性・中立性・信頼性の向上にご協力ください。<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%83%9D%E3%83%86%E3%83%B3%E3%82%B7%E3%83%A3%E3%83%AB%22&num=50">"ポテンシャル"</a> – <a rel="nofollow" class="external text" href="//www.google.co.jp/search?hl=ja&q=%22%E3%83%9D%E3%83%86%E3%83%B3%E3%82%B7%E3%83%A3%E3%83%AB%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%83%9D%E3%83%86%E3%83%B3%E3%82%B7%E3%83%A3%E3%83%AB%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%83%9D%E3%83%86%E3%83%B3%E3%82%B7%E3%83%A3%E3%83%AB%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%83%9D%E3%83%86%E3%83%B3%E3%82%B7%E3%83%A3%E3%83%AB%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%83%9D%E3%83%86%E3%83%B3%E3%82%B7%E3%83%A3%E3%83%AB%22">J-STAGE</a> <b>·</b> <a rel="nofollow" class="external text" href="https://ndlsearch.ndl.go.jp/api/openurl?any=%22%E3%83%9D%E3%83%86%E3%83%B3%E3%82%B7%E3%83%A3%E3%83%AB%22">NDL</a> <b>·</b> <a rel="nofollow" class="external text" href="https://dlib.jp/?q=%22%E3%83%9D%E3%83%86%E3%83%B3%E3%82%B7%E3%83%A3%E3%83%AB%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%83%9D%E3%83%86%E3%83%B3%E3%82%B7%E3%83%A3%E3%83%AB%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="2019年4月">2019年4月</span></span>)</i></span></div></td></tr></tbody></table> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r101304250"><table class="box-参照方法 plainlinks metadata ambox ambox-content" 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/a/a1/2017-fr.wp-orange-source.svg/45px-2017-fr.wp-orange-source.svg.png" decoding="async" width="45" height="45" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a1/2017-fr.wp-orange-source.svg/68px-2017-fr.wp-orange-source.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a1/2017-fr.wp-orange-source.svg/90px-2017-fr.wp-orange-source.svg.png 2x" data-file-width="512" data-file-height="512" /></span></span></div></td><td class="mbox-text"><div class="mbox-text-span"><b><a href="/wiki/Wikipedia:%E3%82%B9%E3%82%BF%E3%82%A4%E3%83%AB%E3%83%9E%E3%83%8B%E3%83%A5%E3%82%A2%E3%83%AB_(%E3%83%AC%E3%82%A4%E3%82%A2%E3%82%A6%E3%83%88)#参考文献" class="mw-redirect" title="Wikipedia:スタイルマニュアル (レイアウト)">出典</a>は列挙するだけでなく、<a href="/wiki/Help:%E8%84%9A%E6%B3%A8" title="Help:脚注">脚注</a>などを用いて<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#出典の示し方" title="Wikipedia:出典を明記する">どの記述の情報源であるかを明記</a>してください。</b><span class="hide-when-compact"> 記事の<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">信頼性向上</a>にご協力をお願いいたします。<small>（<span title="2019年4月">2019年4月</span>）</small></span></div></td></tr></tbody></table> <style data-mw-deduplicate="TemplateStyles:r101346560">.mw-parser-output .hatnote{margin:0.5em 0;padding:3px 2em;background-color:transparent;border-bottom:1px solid #a2a9b1;font-size:90%}html.skin-theme-clientpref-night .mw-parser-output .hatnote>table{color:inherit}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .hatnote>table{color:inherit}}</style><div class="hatnote dablink noprint"><table style="width:100%; background:transparent;"> <tbody><tr><td style="width:25px;"><span typeof="mw:File"><a href="/wiki/%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB:Disambig_gray.svg" class="mw-file-description" title="曖昧さ回避"><img alt="曖昧さ回避" src="//upload.wikimedia.org/wikipedia/commons/thumb/5/5f/Disambig_gray.svg/25px-Disambig_gray.svg.png" decoding="async" width="25" height="19" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/5f/Disambig_gray.svg/38px-Disambig_gray.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/5f/Disambig_gray.svg/50px-Disambig_gray.svg.png 2x" data-file-width="220" data-file-height="168" /></a></span></td> <td>「<b>Potential</b>」はこの項目へ<a href="/wiki/Wikipedia:%E3%83%AA%E3%83%80%E3%82%A4%E3%83%AC%E3%82%AF%E3%83%88" title="Wikipedia:リダイレクト">転送</a>されています。<a href="/wiki/%E9%8C%A6%E6%88%B8%E4%BA%AE" title="錦戸亮">錦戸亮</a>の楽曲については「<a href="/wiki/NOMAD_(%E9%8C%A6%E6%88%B8%E4%BA%AE%E3%81%AE%E3%82%A2%E3%83%AB%E3%83%90%E3%83%A0)" title="NOMAD (錦戸亮のアルバム)">NOMAD (錦戸亮のアルバム)</a>」をご覧ください。</td> </tr></tbody></table></div> <p><b>ポテンシャル</b>（<a href="/wiki/%E8%8B%B1%E8%AA%9E" title="英語">英</a>: <span lang="en">potential</span>）は、潜在力、潜在性を意味する<a href="/wiki/%E7%89%A9%E7%90%86" class="mw-redirect" title="物理">物理</a>用語。 </p><p>最初にポテンシャル（<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>）の考え方を導入したのは、<a href="/wiki/%E3%82%B8%E3%83%A7%E3%82%BC%E3%83%95%EF%BC%9D%E3%83%AB%E3%82%A4%E3%83%BB%E3%83%A9%E3%82%B0%E3%83%A9%E3%83%B3%E3%82%B8%E3%83%A5" title="ジョゼフ＝ルイ・ラグランジュ">ジョゼフ＝ルイ・ラグランジュ</a>である（<a href="/wiki/1773%E5%B9%B4" title="1773年">1773年</a>）。ラグランジュの段階ではポテンシャルとは言われておらず、これをポテンシャルと呼んだのは、<a href="/wiki/%E3%82%B8%E3%83%A7%E3%83%BC%E3%82%B8%E3%83%BB%E3%82%B0%E3%83%AA%E3%83%BC%E3%83%B3" title="ジョージ・グリーン">ジョージ・グリーン</a>である（<a href="/wiki/1828%E5%B9%B4" title="1828年">1828年</a>）。<a href="/wiki/%E3%82%AB%E3%83%BC%E3%83%AB%E3%83%BB%E3%83%95%E3%83%AA%E3%83%BC%E3%83%89%E3%83%AA%E3%83%92%E3%83%BB%E3%82%AC%E3%82%A6%E3%82%B9" title="カール・フリードリヒ・ガウス">カール・フリードリヒ・ガウス</a>、<a href="/wiki/%E3%82%A6%E3%82%A3%E3%83%AA%E3%82%A2%E3%83%A0%E3%83%BB%E3%83%88%E3%83%A0%E3%82%BD%E3%83%B3" title="ウィリアム・トムソン">ウィリアム・トムソン</a>、<a href="/wiki/%E3%83%9A%E3%83%BC%E3%82%BF%E3%83%BC%E3%83%BB%E3%82%B0%E3%82%B9%E3%82%BF%E3%83%95%E3%83%BB%E3%83%87%E3%82%A3%E3%83%AA%E3%82%AF%E3%83%AC" title="ペーター・グスタフ・ディリクレ">ペーター・グスタフ・ディリクレ</a>によってポテンシャル論における三つの基本問題として、<a href="/wiki/%E3%83%87%E3%82%A3%E3%83%AA%E3%82%AF%E3%83%AC%E5%95%8F%E9%A1%8C" title="ディリクレ問題">ディリクレ問題</a>、ノイマン問題、斜交微分の問題が注目されるようになった。 </p><p>ポテンシャルエネルギー（<a href="/wiki/%E4%BD%8D%E7%BD%AE%E3%82%A8%E3%83%8D%E3%83%AB%E3%82%AE%E3%83%BC" title="位置エネルギー">位置エネルギー</a>）のことをポテンシャルと呼ぶこともある。 </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="ポテンシャル（狭義）"><span id=".E3.83.9D.E3.83.86.E3.83.B3.E3.82.B7.E3.83.A3.E3.83.AB.EF.BC.88.E7.8B.AD.E7.BE.A9.EF.BC.89"></span>ポテンシャル（狭義）</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E3%83%9D%E3%83%86%E3%83%B3%E3%82%B7%E3%83%A3%E3%83%AB&action=edit&section=1" title="節を編集: ポテンシャル（狭義）"><span>編集</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/%E7%A9%BA%E9%96%93" title="空間">空間</a>内において、空間内の各点に働く<a href="/wiki/%E5%8A%9B_(%E7%89%A9%E7%90%86%E5%AD%A6)" title="力 (物理学)">力</a> <i><b>F</b></i> が、当該点上のある定まった量 <i>V</i> から、 </p> <div style="margin-top:1ex; margin-left:2em; margin-bottom:1ex;"> <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 {\boldsymbol {F}}=-\nabla V(=-\operatorname {grad} V)\qquad \cdots (1)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">F</mi> </mrow> <mo>=</mo> <mo>−</mo> <mi mathvariant="normal">∇</mi> <mi>V</mi> <mo stretchy="false">(</mo> <mo>=</mo> <mo>−</mo> <mi>grad</mi> <mo>⁡</mo> <mi>V</mi> <mo stretchy="false">)</mo> <mspace width="2em" /> <mo>⋯</mo> <mo stretchy="false">(</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\boldsymbol {F}}=-\nabla V(=-\operatorname {grad} V)\qquad \cdots (1)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/eb128cccc0f4b620b85011299403d94da1c2f669" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:34.785ex; height:2.843ex;" alt="{\displaystyle {\boldsymbol {F}}=-\nabla V(=-\operatorname {grad} V)\qquad \cdots (1)}"></span> </p> </div> <p>として求まる時、<i>V</i> を力 <i><b>F</b></i> の<b>ポテンシャル</b>と言う。上式の関係より、<i>V</i> は勾配におけるスカラーポテンシャルである。なお、gradは<a href="/wiki/%E5%8B%BE%E9%85%8D_(%E3%83%99%E3%82%AF%E3%83%88%E3%83%AB%E8%A7%A3%E6%9E%90)" title="勾配 (ベクトル解析)">勾配</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 \nabla }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∇</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \nabla }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a3d0e93b78c50237f9ea83d027e4ebbdaef354b2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.936ex; height:2.176ex;" alt="{\displaystyle \nabla }"></span>は<a href="/wiki/%E3%83%8A%E3%83%96%E3%83%A9" title="ナブラ">ナブラ</a>である。 </p><p>一つの<a href="/wiki/%E8%B3%AA%E7%82%B9" title="質点">質点</a>を考え、これが力 <i><b>F</b></i> の作用する<a href="/wiki/%E5%A0%B4" title="場">場</a>（力場）にあり、当該質点が d<i><b>l</b></i> =(d<i>x</i> , d<i>y</i> , d<i>z</i>)だけ<a href="/wiki/%E5%A4%89%E4%BD%8D" title="変位">変位</a>した時、その力のなした<a href="/wiki/%E4%BB%95%E4%BA%8B_(%E7%89%A9%E7%90%86%E5%AD%A6)" title="仕事 (物理学)">仕事</a> d<i>W</i> は（以下、<a href="/wiki/%E7%9B%B4%E4%BA%A4%E5%BA%A7%E6%A8%99%E7%B3%BB" title="直交座標系">直交座標系</a>を考える）、 </p> <div style="margin-top:1ex; margin-left:2em; margin-bottom:1ex;"> <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 \mathrm {d} W={\boldsymbol {F}}\cdot \mathrm {d} {\boldsymbol {l}}=F_{x}\mathrm {d} x+F_{y}\mathrm {d} y+F_{z}\mathrm {d} z}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>W</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">F</mi> </mrow> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">l</mi> </mrow> <mo>=</mo> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>x</mi> <mo>+</mo> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>y</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>y</mi> <mo>+</mo> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>z</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>z</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {d} W={\boldsymbol {F}}\cdot \mathrm {d} {\boldsymbol {l}}=F_{x}\mathrm {d} x+F_{y}\mathrm {d} y+F_{z}\mathrm {d} z}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/101064e692a3722a650243833751129a1f3b934b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:36.425ex; height:2.843ex;" alt="{\displaystyle \mathrm {d} W={\boldsymbol {F}}\cdot \mathrm {d} {\boldsymbol {l}}=F_{x}\mathrm {d} x+F_{y}\mathrm {d} y+F_{z}\mathrm {d} z}"></span> </p> </div> <p>となる。(<i>F<sub>x</sub></i> , <i>F<sub>y</sub></i> , <i>F<sub>z</sub></i>)は力 <i><b>F</b></i> の各座標成分である。ポテンシャルに関して、 </p> <div style="margin-top:1ex; margin-left:2em; margin-bottom:1ex;"> <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 F_{x}=-{\partial V \over {\partial x}},\quad F_{y}=-{\partial V \over {\partial y}},\quad F_{z}=-{\partial V \over {\partial z}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msub> <mo>=</mo> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>V</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> <mi>x</mi> </mrow> </mfrac> </mrow> <mo>,</mo> <mspace width="1em" /> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>y</mi> </mrow> </msub> <mo>=</mo> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>V</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> <mi>y</mi> </mrow> </mfrac> </mrow> <mo>,</mo> <mspace width="1em" /> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>z</mi> </mrow> </msub> <mo>=</mo> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>V</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> <mi>z</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F_{x}=-{\partial V \over {\partial x}},\quad F_{y}=-{\partial V \over {\partial y}},\quad F_{z}=-{\partial V \over {\partial z}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/04b606406e36d0d8e1562a366c0ddab4e4473163" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:40.964ex; height:6.009ex;" alt="{\displaystyle F_{x}=-{\partial V \over {\partial x}},\quad F_{y}=-{\partial V \over {\partial y}},\quad F_{z}=-{\partial V \over {\partial z}}}"></span> </p> </div> <p>と表現できるなら、 </p> <div style="margin-top:1ex; margin-left:2em; margin-bottom:1ex;"> <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 \mathrm {d} W=-{\partial V \over {\partial x}}\mathrm {d} x-{\partial V \over {\partial y}}\mathrm {d} y-{\partial V \over {\partial z}}\mathrm {d} z=-\mathrm {d} V}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>W</mi> <mo>=</mo> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>V</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> <mi>x</mi> </mrow> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>x</mi> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>V</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> <mi>y</mi> </mrow> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>y</mi> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>V</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> <mi>z</mi> </mrow> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>z</mi> <mo>=</mo> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>V</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {d} W=-{\partial V \over {\partial x}}\mathrm {d} x-{\partial V \over {\partial y}}\mathrm {d} y-{\partial V \over {\partial z}}\mathrm {d} z=-\mathrm {d} V}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/40c6f74b786c4f4a513be2351a513d4a17f1c381" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:41.577ex; height:6.009ex;" alt="{\displaystyle \mathrm {d} W=-{\partial V \over {\partial x}}\mathrm {d} x-{\partial V \over {\partial y}}\mathrm {d} y-{\partial V \over {\partial z}}\mathrm {d} z=-\mathrm {d} V}"></span> </p> </div> <p>となる。 </p> <div class="mw-heading mw-heading2"><h2 id="保存力"><span id=".E4.BF.9D.E5.AD.98.E5.8A.9B"></span>保存力</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E3%83%9D%E3%83%86%E3%83%B3%E3%82%B7%E3%83%A3%E3%83%AB&action=edit&section=2" title="節を編集: 保存力"><span>編集</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>力の作用する範囲内で質点が、位置AからBへ運動する間になす仕事 <i>W</i><sub>A-B</sub> は、 </p> <div style="margin-top:1ex; margin-left:2em; margin-bottom:1ex;"> <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 W_{\mathrm {A-B} }\,=V_{\mathrm {A} }-V_{\mathrm {B} }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>W</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">A</mi> <mo>−</mo> <mi mathvariant="normal">B</mi> </mrow> </mrow> </msub> <mspace width="thinmathspace" /> <mo>=</mo> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">A</mi> </mrow> </mrow> </msub> <mo>−</mo> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">B</mi> </mrow> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle W_{\mathrm {A-B} }\,=V_{\mathrm {A} }-V_{\mathrm {B} }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d20c18a8dabcdc79403a92260ebb6253898414c8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:17.998ex; height:2.676ex;" alt="{\displaystyle W_{\mathrm {A-B} }\,=V_{\mathrm {A} }-V_{\mathrm {B} }}"></span> </p> </div> <p>となる。<i>V</i><sub>A</sub> は位置Aでのポテンシャル、<i>V</i><sub>B</sub> は位置Bでのポテンシャルである。この結果は、質点の動いた経路に依らない。どのような経路を通るかに関わらず、なした仕事がどの経路でも等しい場合、この時に質点に働く力を<b>保存力</b>（conservative force）と言う。また、保存力のみが作用する場（力場）を<b>保存力場</b>（conservative force field）と言う。また保存力では、質点が位置Aから出発して位置Aに戻る経路（閉じた経路）の場合、質点のなした仕事は、途中の通った道筋に関係なくゼロとなる。 </p><p>このように（スカラー）ポテンシャルによる力は保存力となる。また、逆に保存力は必ずポテンシャルを伴うことが言える。 </p> <div class="mw-heading mw-heading2"><h2 id="ベクトルポテンシャル"><span id=".E3.83.99.E3.82.AF.E3.83.88.E3.83.AB.E3.83.9D.E3.83.86.E3.83.B3.E3.82.B7.E3.83.A3.E3.83.AB"></span>ベクトルポテンシャル</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E3%83%9D%E3%83%86%E3%83%B3%E3%82%B7%E3%83%A3%E3%83%AB&action=edit&section=3" title="節を編集: ベクトルポテンシャル"><span>編集</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="rellink" style="margin-bottom: 0.5em; padding-left: 2em; font-size: 90%;" role="note">→詳細は「<a href="/wiki/%E3%83%99%E3%82%AF%E3%83%88%E3%83%AB%E3%83%9D%E3%83%86%E3%83%B3%E3%82%B7%E3%83%A3%E3%83%AB" title="ベクトルポテンシャル">ベクトルポテンシャル</a>」を参照</div> <div class="mw-heading mw-heading2"><h2 id="ポテンシャルエネルギー"><span id=".E3.83.9D.E3.83.86.E3.83.B3.E3.82.B7.E3.83.A3.E3.83.AB.E3.82.A8.E3.83.8D.E3.83.AB.E3.82.AE.E3.83.BC"></span>ポテンシャルエネルギー</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E3%83%9D%E3%83%86%E3%83%B3%E3%82%B7%E3%83%A3%E3%83%AB&action=edit&section=4" title="節を編集: ポテンシャルエネルギー"><span>編集</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>式(1)について、<i><b>F</b></i> は力なので、これに関しての質量 <i>m</i> の質点（簡単のため1質点を想定）の<a href="/wiki/%E3%83%8B%E3%83%A5%E3%83%BC%E3%83%88%E3%83%B3%E3%81%AE%E9%81%8B%E5%8B%95%E6%96%B9%E7%A8%8B%E5%BC%8F" title="ニュートンの運動方程式">運動方程式</a>は、 </p> <div style="margin-top:1ex; margin-left:2em; margin-bottom:1ex;"> <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 {\boldsymbol {F}}=m{\mathrm {d} ^{2}{\boldsymbol {r}} \over {\mathrm {d} t^{2}}}=-\nabla V}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">F</mi> </mrow> <mo>=</mo> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">r</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msup> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>=</mo> <mo>−</mo> <mi mathvariant="normal">∇</mi> <mi>V</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\boldsymbol {F}}=m{\mathrm {d} ^{2}{\boldsymbol {r}} \over {\mathrm {d} t^{2}}}=-\nabla V}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5ea11f1b5bd9e24bc2b8b8ced373d526d8a7ccdc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:20.061ex; height:6.009ex;" alt="{\displaystyle {\boldsymbol {F}}=m{\mathrm {d} ^{2}{\boldsymbol {r}} \over {\mathrm {d} t^{2}}}=-\nabla V}"></span> </p> </div> <p>となる。d<sup>2</sup><i><b>r</b></i> /d<i>t</i> <sup>2</sup> は質点の加速度である。真中と右辺にそれぞれ d<i><b>r</b></i> /d<i>t</i> をかけ、時間 <i>t</i> で積分すると次の式を得る。 </p> <div style="margin-top:1ex; margin-left:2em; margin-bottom:1ex;"> <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 {1 \over 2}m\left({\mathrm {d} {\boldsymbol {r}} \over {\mathrm {d} t}}\right)^{2}+V({\boldsymbol {r}})=\mathrm {constant} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <mi>m</mi> <msup> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">r</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>t</mi> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mi>V</mi> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">r</mi> </mrow> <mo stretchy="false">)</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">c</mi> <mi mathvariant="normal">o</mi> <mi mathvariant="normal">n</mi> <mi mathvariant="normal">s</mi> <mi mathvariant="normal">t</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">n</mi> <mi mathvariant="normal">t</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {1 \over 2}m\left({\mathrm {d} {\boldsymbol {r}} \over {\mathrm {d} t}}\right)^{2}+V({\boldsymbol {r}})=\mathrm {constant} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f34c4862715d35053cdd79a6e047d73e95c6b24a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:31.306ex; height:6.509ex;" alt="{\displaystyle {1 \over 2}m\left({\mathrm {d} {\boldsymbol {r}} \over {\mathrm {d} t}}\right)^{2}+V({\boldsymbol {r}})=\mathrm {constant} }"></span> </p> </div> <p>これは、 </p> <div style="margin-top:1ex; margin-left:2em; margin-bottom:1ex;"> <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 {\mathrm {d} \over {\mathrm {d} t}}\left({\mathrm {d} {\boldsymbol {r}} \over {\mathrm {d} t}}\right)^{2}=2{\mathrm {d} {\boldsymbol {r}} \over {\mathrm {d} t}}\cdot {\mathrm {d} ^{2}{\boldsymbol {r}} \over {\mathrm {d} t^{2}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>t</mi> </mrow> </mfrac> </mrow> <msup> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">r</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>t</mi> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">r</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>t</mi> </mrow> </mfrac> </mrow> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">r</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msup> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathrm {d} \over {\mathrm {d} t}}\left({\mathrm {d} {\boldsymbol {r}} \over {\mathrm {d} t}}\right)^{2}=2{\mathrm {d} {\boldsymbol {r}} \over {\mathrm {d} t}}\cdot {\mathrm {d} ^{2}{\boldsymbol {r}} \over {\mathrm {d} t^{2}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a9e2204bbcab5af672e740479237b69e2ca6f865" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:24.513ex; height:6.509ex;" alt="{\displaystyle {\mathrm {d} \over {\mathrm {d} t}}\left({\mathrm {d} {\boldsymbol {r}} \over {\mathrm {d} t}}\right)^{2}=2{\mathrm {d} {\boldsymbol {r}} \over {\mathrm {d} t}}\cdot {\mathrm {d} ^{2}{\boldsymbol {r}} \over {\mathrm {d} t^{2}}}}"></span> </p> </div> <p>及び、 </p> <div style="margin-top:1ex; margin-left:2em; margin-bottom:1ex;"> <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 {\mathrm {d} \over {\mathrm {d} t}}V({\boldsymbol {r}})={\mathrm {d} {\boldsymbol {r}} \over {\mathrm {d} t}}\cdot \nabla V({\boldsymbol {r}})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>t</mi> </mrow> </mfrac> </mrow> <mi>V</mi> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">r</mi> </mrow> <mo stretchy="false">)</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">r</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>t</mi> </mrow> </mfrac> </mrow> <mo>⋅</mo> <mi mathvariant="normal">∇</mi> <mi>V</mi> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">r</mi> </mrow> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathrm {d} \over {\mathrm {d} t}}V({\boldsymbol {r}})={\mathrm {d} {\boldsymbol {r}} \over {\mathrm {d} t}}\cdot \nabla V({\boldsymbol {r}})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1c8e6649189e4f553cdde91e182a6784aa3f248a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:22.693ex; height:5.509ex;" alt="{\displaystyle {\mathrm {d} \over {\mathrm {d} t}}V({\boldsymbol {r}})={\mathrm {d} {\boldsymbol {r}} \over {\mathrm {d} t}}\cdot \nabla V({\boldsymbol {r}})}"></span> </p> </div> <p>から求められる。constantは時間 <i>t</i> に関しての積分から出てくる<a href="/wiki/%E7%A9%8D%E5%88%86%E5%AE%9A%E6%95%B0" class="mw-redirect" title="積分定数">定数</a>である。これは積分して得られた式の左辺において、第一項が<a href="/wiki/%E9%81%8B%E5%8B%95%E3%82%A8%E3%83%8D%E3%83%AB%E3%82%AE%E3%83%BC" title="運動エネルギー">運動エネルギー</a>であり、それと第二項の <i>V</i> (<i><b>r</b></i>)との和が一定であることを意味し、この場合、<i>V</i> (<i><b>r</b></i>)のことを<b>ポテンシャルエネルギー</b>（<a href="/wiki/%E4%BD%8D%E7%BD%AE%E3%82%A8%E3%83%8D%E3%83%AB%E3%82%AE%E3%83%BC" title="位置エネルギー">位置エネルギー</a>）と呼ぶ。形式上ポテンシャルと同じ形だが、この時の<i>V</i> (<i><b>r</b></i>)の<i><b>r</b></i> は質点の位置であり、<i><b>r</b></i> = <i><b>r</b></i> (<i>t</i>)である。 </p> <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%83%9D%E3%83%86%E3%83%B3%E3%82%B7%E3%83%A3%E3%83%AB&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> <ul><li><cite style="font-style:normal" class="citation" id="CITEREF日本数学会1985">日本数学会『岩波数学辞典（第3版）』岩波書店、1985年。<style data-mw-deduplicate="TemplateStyles:r101121245">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation.cs-ja1 q,.mw-parser-output .citation.cs-ja2 q{quotes:"「""」""『""』"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free a,.mw-parser-output .citation .cs1-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited 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:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription a,.mw-parser-output .citation .cs1-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:var(--color-success,#3a3);margin-left:0.3em}.mw-parser-output .cs1-format{font-size:95%}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}</style><a href="/wiki/ISBN" title="ISBN">ISBN</a> <a href="/wiki/%E7%89%B9%E5%88%A5:%E6%96%87%E7%8C%AE%E8%B3%87%E6%96%99/4000800167" title="特別:文献資料/4000800167">4000800167</a>。</cite><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=%E5%B2%A9%E6%B3%A2%E6%95%B0%E5%AD%A6%E8%BE%9E%E5%85%B8%EF%BC%88%E7%AC%AC3%E7%89%88%EF%BC%89&rft.aulast=%E6%97%A5%E6%9C%AC%E6%95%B0%E5%AD%A6%E4%BC%9A&rft.au=%E6%97%A5%E6%9C%AC%E6%95%B0%E5%AD%A6%E4%BC%9A&rft.date=1985&rft.pub=%E5%B2%A9%E6%B3%A2%E6%9B%B8%E5%BA%97&rft.isbn=4000800167&rfr_id=info:sid/ja.wikipedia.org:%E3%83%9D%E3%83%86%E3%83%B3%E3%82%B7%E3%83%A3%E3%83%AB"><span style="display: none;"> </span></span></li></ul> <div class="mw-heading mw-heading2"><h2 id="関連記事"><span id=".E9.96.A2.E9.80.A3.E8.A8.98.E4.BA.8B"></span>関連記事</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E3%83%9D%E3%83%86%E3%83%B3%E3%82%B7%E3%83%A3%E3%83%AB&action=edit&section=6" title="節を編集: 関連記事"><span>編集</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/%E3%83%87%E3%82%A3%E3%83%AA%E3%82%AF%E3%83%AC%E5%95%8F%E9%A1%8C" title="ディリクレ問題">ディリクレ問題</a></li> <li><a href="/wiki/%E8%AA%BF%E5%92%8C%E9%96%A2%E6%95%B0" title="調和関数">調和関数</a></li> <li><a href="/wiki/%E3%83%98%E3%83%AB%E3%83%A0%E3%83%9B%E3%83%AB%E3%83%84%E3%81%AE%E5%AE%9A%E7%90%86" title="ヘルムホルツの定理">ヘルムホルツの定理</a></li></ul> <div class="mw-heading mw-heading3"><h3 id="その他のポテンシャル"><span id=".E3.81.9D.E3.81.AE.E4.BB.96.E3.81.AE.E3.83.9D.E3.83.86.E3.83.B3.E3.82.B7.E3.83.A3.E3.83.AB"></span>その他のポテンシャル</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E3%83%9D%E3%83%86%E3%83%B3%E3%82%B7%E3%83%A3%E3%83%AB&action=edit&section=7" title="節を編集: その他のポテンシャル"><span>編集</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/%E6%B0%B4%E3%83%9D%E3%83%86%E3%83%B3%E3%82%B7%E3%83%A3%E3%83%AB" title="水ポテンシャル">水ポテンシャル</a></li> <li><a href="/wiki/%E7%86%B1%E5%8A%9B%E5%AD%A6%E3%83%9D%E3%83%86%E3%83%B3%E3%82%B7%E3%83%A3%E3%83%AB" title="熱力学ポテンシャル">熱力学ポテンシャル</a></li> <li><a href="/wiki/%E5%8C%96%E5%AD%A6%E3%83%9D%E3%83%86%E3%83%B3%E3%82%B7%E3%83%A3%E3%83%AB" title="化学ポテンシャル">化学ポテンシャル</a></li> <li><a href="/wiki/%E6%B9%AF%E5%B7%9D%E3%83%9D%E3%83%86%E3%83%B3%E3%82%B7%E3%83%A3%E3%83%AB" title="湯川ポテンシャル">湯川ポテンシャル</a></li> <li><a href="/wiki/%E6%93%AC%E3%83%9D%E3%83%86%E3%83%B3%E3%82%B7%E3%83%A3%E3%83%AB" title="擬ポテンシャル">擬ポテンシャル</a></li> <li><a href="/wiki/2%E4%BD%93%E3%83%9D%E3%83%86%E3%83%B3%E3%82%B7%E3%83%A3%E3%83%AB" title="2体ポテンシャル">2体ポテンシャル</a></li> <li><a href="/wiki/%E9%80%9F%E5%BA%A6%E3%83%9D%E3%83%86%E3%83%B3%E3%82%B7%E3%83%A3%E3%83%AB" title="速度ポテンシャル">速度ポテンシャル</a>、<a href="/wiki/%E8%A4%87%E7%B4%A0%E9%80%9F%E5%BA%A6%E3%83%9D%E3%83%86%E3%83%B3%E3%82%B7%E3%83%A3%E3%83%AB" title="複素速度ポテンシャル">複素速度ポテンシャル</a> - <a href="/wiki/%E6%B5%81%E4%BD%93%E5%8A%9B%E5%AD%A6" title="流体力学">流体力学</a>において速度場を導くポテンシャル。</li></ul>    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