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Elérhető 44 nyelven" > <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-44" 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">44 nyelv</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Fermi%E2%80%93Dirac_statistics" title="Fermi–Dirac statistics – angol" lang="en" hreflang="en" data-title="Fermi–Dirac statistics" data-language-autonym="English" data-language-local-name="angol" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%A5%D8%AD%D8%B5%D8%A7%D8%A1_%D9%81%D9%8A%D8%B1%D9%85%D9%8A_%D9%88%D8%AF%D9%8A%D8%B1%D8%A7%D9%83" title="إحصاء فيرمي وديراك – arab" lang="ar" hreflang="ar" data-title="إحصاء فيرمي وديراك" data-language-autonym="العربية" data-language-local-name="arab" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Fermi%E2%80%93Dirak_statistikas%C4%B1" title="Fermi–Dirak statistikası – azerbajdzsáni" lang="az" hreflang="az" data-title="Fermi–Dirak statistikası" data-language-autonym="Azərbaycanca" data-language-local-name="azerbajdzsáni" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%A1%D1%82%D0%B0%D1%82%D1%8B%D1%81%D1%82%D1%8B%D0%BA%D0%B0_%D0%A4%D0%B5%D1%80%D0%BC%D1%96_%E2%80%94_%D0%94%D0%B7%D1%96%D1%80%D0%B0%D0%BA%D0%B0" title="Статыстыка Фермі — Дзірака – belarusz" lang="be" hreflang="be" data-title="Статыстыка Фермі — Дзірака" data-language-autonym="Беларуская" data-language-local-name="belarusz" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%A1%D1%82%D0%B0%D1%82%D0%B8%D1%81%D1%82%D0%B8%D0%BA%D0%B0_%D0%BD%D0%B0_%D0%A4%D0%B5%D1%80%D0%BC%D0%B8-%D0%94%D0%B8%D1%80%D0%B0%D0%BA" title="Статистика на Ферми-Дирак – bolgár" lang="bg" hreflang="bg" data-title="Статистика на Ферми-Дирак" data-language-autonym="Български" data-language-local-name="bolgár" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%AB%E0%A7%87%E0%A6%B0%E0%A7%8D%E0%A6%AE%E0%A6%BF%E2%80%93%E0%A6%A1%E0%A6%BF%E0%A6%B0%E2%80%8D%E0%A7%8D%E0%A6%AF%E0%A6%BE%E0%A6%95_%E0%A6%AA%E0%A6%B0%E0%A6%BF%E0%A6%B8%E0%A6%82%E0%A6%96%E0%A7%8D%E0%A6%AF%E0%A6%BE%E0%A6%A8" title="ফের্মি–ডির‍্যাক পরিসংখ্যান – bangla" lang="bn" hreflang="bn" data-title="ফের্মি–ডির‍্যাক পরিসংখ্যান" data-language-autonym="বাংলা" data-language-local-name="bangla" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Fermi%E2%80%93Diracova_statistika" title="Fermi–Diracova statistika – bosnyák" lang="bs" hreflang="bs" data-title="Fermi–Diracova statistika" data-language-autonym="Bosanski" data-language-local-name="bosnyák" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Estad%C3%ADstica_de_Fermi-Dirac" title="Estadística de Fermi-Dirac – katalán" lang="ca" hreflang="ca" data-title="Estadística de Fermi-Dirac" data-language-autonym="Català" data-language-local-name="katalán" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Fermiho%E2%80%93Diracovo_rozd%C4%9Blen%C3%AD" title="Fermiho–Diracovo rozdělení – cseh" lang="cs" hreflang="cs" data-title="Fermiho–Diracovo rozdělení" data-language-autonym="Čeština" data-language-local-name="cseh" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Fermi-Dirac-Statistik" title="Fermi-Dirac-Statistik – német" lang="de" hreflang="de" data-title="Fermi-Dirac-Statistik" data-language-autonym="Deutsch" data-language-local-name="német" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Statistiko_Fermi%E2%80%93Dirac" title="Statistiko Fermi–Dirac – eszperantó" lang="eo" hreflang="eo" data-title="Statistiko Fermi–Dirac" data-language-autonym="Esperanto" data-language-local-name="eszperantó" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Estad%C3%ADstica_de_Fermi-Dirac" title="Estadística de Fermi-Dirac – spanyol" lang="es" hreflang="es" data-title="Estadística de Fermi-Dirac" data-language-autonym="Español" data-language-local-name="spanyol" 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/Fermi-Diraci_statistika" title="Fermi-Diraci statistika – észt" lang="et" hreflang="et" data-title="Fermi-Diraci statistika" data-language-autonym="Eesti" data-language-local-name="észt" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Fermi-Diracen_estatistika" title="Fermi-Diracen estatistika – baszk" lang="eu" hreflang="eu" data-title="Fermi-Diracen estatistika" data-language-autonym="Euskara" data-language-local-name="baszk" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%A2%D9%85%D8%A7%D8%B1_%D9%81%D8%B1%D9%85%DB%8C-%D8%AF%DB%8C%D8%B1%D8%A7%DA%A9" title="آمار فرمی-دیراک – perzsa" lang="fa" hreflang="fa" data-title="آمار فرمی-دیراک" data-language-autonym="فارسی" data-language-local-name="perzsa" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Fermin%E2%80%93Diracin_statistiikka" title="Fermin–Diracin statistiikka – finn" lang="fi" hreflang="fi" data-title="Fermin–Diracin statistiikka" data-language-autonym="Suomi" data-language-local-name="finn" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Statistique_de_Fermi-Dirac" title="Statistique de Fermi-Dirac – francia" lang="fr" hreflang="fr" data-title="Statistique de Fermi-Dirac" data-language-autonym="Français" data-language-local-name="francia" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/Staitistic_Fermi-Dirac" title="Staitistic Fermi-Dirac – ír" lang="ga" hreflang="ga" data-title="Staitistic Fermi-Dirac" data-language-autonym="Gaeilge" data-language-local-name="ír" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%94%D7%AA%D7%A4%D7%9C%D7%92%D7%95%D7%AA_%D7%A4%D7%A8%D7%9E%D7%99-%D7%93%D7%99%D7%A8%D7%90%D7%A7" title="התפלגות פרמי-דיראק – héber" lang="he" hreflang="he" data-title="התפלגות פרמי-דיראק" data-language-autonym="עברית" data-language-local-name="héber" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Fermi-Diracova_statistika" title="Fermi-Diracova statistika – horvát" lang="hr" hreflang="hr" data-title="Fermi-Diracova statistika" data-language-autonym="Hrvatski" data-language-local-name="horvát" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D5%96%D5%A5%D6%80%D5%B4%D5%AB-%D4%B4%D5%AB%D6%80%D5%A1%D5%AF%D5%AB_%D5%BE%D5%AB%D5%B3%D5%A1%D5%AF%D5%A1%D5%A3%D6%80%D5%B8%D6%82%D5%A9%D5%B5%D5%B8%D6%82%D5%B6" title="Ֆերմի-Դիրակի վիճակագրություն – örmény" lang="hy" hreflang="hy" data-title="Ֆերմի-Դիրակի վիճակագրություն" data-language-autonym="Հայերեն" data-language-local-name="örmény" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Statistik_Fermi-Dirac" title="Statistik Fermi-Dirac – indonéz" lang="id" hreflang="id" data-title="Statistik Fermi-Dirac" data-language-autonym="Bahasa Indonesia" data-language-local-name="indonéz" 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/Statistica_di_Fermi-Dirac" title="Statistica di Fermi-Dirac – olasz" lang="it" hreflang="it" data-title="Statistica di Fermi-Dirac" data-language-autonym="Italiano" data-language-local-name="olasz" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E3%83%95%E3%82%A7%E3%83%AB%E3%83%9F%E5%88%86%E5%B8%83%E9%96%A2%E6%95%B0" title="フェルミ分布関数 – japán" lang="ja" hreflang="ja" data-title="フェルミ分布関数" data-language-autonym="日本語" data-language-local-name="japán" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%ED%8E%98%EB%A5%B4%EB%AF%B8-%EB%94%94%EB%9E%99_%ED%86%B5%EA%B3%84" title="페르미-디랙 통계 – koreai" lang="ko" hreflang="ko" data-title="페르미-디랙 통계" data-language-autonym="한국어" data-language-local-name="koreai" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Fermi-Diracstatistiek" title="Fermi-Diracstatistiek – holland" lang="nl" hreflang="nl" data-title="Fermi-Diracstatistiek" data-language-autonym="Nederlands" data-language-local-name="holland" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Fermi-Dirac-statistikk" title="Fermi-Dirac-statistikk – norvég (nynorsk)" lang="nn" hreflang="nn" data-title="Fermi-Dirac-statistikk" data-language-autonym="Norsk nynorsk" data-language-local-name="norvég (nynorsk)" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Fermi-Dirac_statistikk" title="Fermi-Dirac statistikk – norvég (bokmål)" lang="nb" hreflang="nb" data-title="Fermi-Dirac statistikk" data-language-autonym="Norsk bokmål" data-language-local-name="norvég (bokmål)" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Statystyka_Fermiego-Diraca" title="Statystyka Fermiego-Diraca – lengyel" lang="pl" hreflang="pl" data-title="Statystyka Fermiego-Diraca" data-language-autonym="Polski" data-language-local-name="lengyel" 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/Estat%C3%ADstica_de_Fermi-Dirac" title="Estatística de Fermi-Dirac – portugál" lang="pt" hreflang="pt" data-title="Estatística de Fermi-Dirac" data-language-autonym="Português" data-language-local-name="portugál" 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%D1%82%D0%B0%D1%82%D0%B8%D1%81%D1%82%D0%B8%D0%BA%D0%B0_%D0%A4%D0%B5%D1%80%D0%BC%D0%B8_%E2%80%94_%D0%94%D0%B8%D1%80%D0%B0%D0%BA%D0%B0" title="Статистика Ферми — Дирака – orosz" lang="ru" hreflang="ru" data-title="Статистика Ферми — Дирака" data-language-autonym="Русский" data-language-local-name="orosz" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Fermi-Diracova_statistika" title="Fermi-Diracova statistika – szerbhorvát" lang="sh" hreflang="sh" data-title="Fermi-Diracova statistika" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="szerbhorvát" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Fermi-Dirac_statistics" title="Fermi-Dirac statistics – Simple English" lang="en-simple" hreflang="en-simple" data-title="Fermi-Dirac statistics" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Fermiho-Diracovo_rozdelenie" title="Fermiho-Diracovo rozdelenie – szlovák" lang="sk" hreflang="sk" data-title="Fermiho-Diracovo rozdelenie" data-language-autonym="Slovenčina" data-language-local-name="szlovák" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Fermi-Diracova_statistika" title="Fermi-Diracova statistika – szlovén" lang="sl" hreflang="sl" data-title="Fermi-Diracova statistika" data-language-autonym="Slovenščina" data-language-local-name="szlovén" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%A4%D0%B5%D1%80%D0%BC%D0%B8-%D0%94%D0%B8%D1%80%D0%B0%D0%BA%D0%BE%D0%B2%D0%B0_%D1%81%D1%82%D0%B0%D1%82%D0%B8%D1%81%D1%82%D0%B8%D0%BA%D0%B0" title="Ферми-Диракова статистика – szerb" lang="sr" hreflang="sr" data-title="Ферми-Диракова статистика" data-language-autonym="Српски / srpski" data-language-local-name="szerb" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Fermi%E2%80%93Dirac-statistik" title="Fermi–Dirac-statistik – svéd" lang="sv" hreflang="sv" data-title="Fermi–Dirac-statistik" data-language-autonym="Svenska" data-language-local-name="svéd" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Fermi-Dirac_istatistikleri" title="Fermi-Dirac istatistikleri – török" lang="tr" hreflang="tr" data-title="Fermi-Dirac istatistikleri" data-language-autonym="Türkçe" data-language-local-name="török" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-tt mw-list-item"><a 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href="https://uz.wikipedia.org/wiki/Fermi_Dirak_statistikasi" title="Fermi Dirak statistikasi – üzbég" lang="uz" hreflang="uz" data-title="Fermi Dirak statistikasi" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="üzbég" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/Th%E1%BB%91ng_k%C3%AA_Fermi%E2%80%93Dirac" title="Thống kê Fermi–Dirac – vietnámi" lang="vi" hreflang="vi" data-title="Thống kê Fermi–Dirac" data-language-autonym="Tiếng Việt" data-language-local-name="vietnámi" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E8%B4%B9%E7%B1%B3-%E7%8B%84%E6%8B%89%E5%85%8B%E7%BB%9F%E8%AE%A1" title="费米-狄拉克统计 – wu kínai" lang="wuu" hreflang="wuu" data-title="费米-狄拉克统计" data-language-autonym="吴语" data-language-local-name="wu kínai" 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id="mw-indicator-indicator-fr-review-status" class="mw-indicator"><indicator name="fr-review-status" class="mw-fr-review-status-indicator" id="mw-fr-revision-toggle"><span class="cdx-fr-css-icon-review--status--stable"></span><b>Ellenőrzött</b></indicator></div> </div> <div id="siteSub" class="noprint">A Wikipédiából, a szabad enciklopédiából</div> </div> <div id="contentSub"><div id="mw-content-subtitle"><div id="mw-fr-revision-messages"><div id="mw-fr-revision-details" class="mw-fr-revision-details-dialog" style="display:none;"><div tabindex="0"></div><div class="cdx-dialog cdx-dialog--horizontal-actions"><header class="cdx-dialog__header cdx-dialog__header--default"><div class="cdx-dialog__header__title-group"><h2 class="cdx-dialog__header__title">Változat állapota</h2><p class="cdx-dialog__header__subtitle">Ez a lap egy ellenőrzött változata</p></div><button class="cdx-button cdx-button--action-default cdx-button--weight-quiet
							cdx-button--size-medium cdx-button--icon-only cdx-dialog__header__close-button" aria-label="Close" onclick="document.getElementById("mw-fr-revision-details").style.display = "none";" type="submit"><span class="cdx-icon cdx-icon--medium
							cdx-fr-css-icon--close"></span></button></header><div class="cdx-dialog__body">Ez a <a href="/wiki/Wikip%C3%A9dia:Jel%C3%B6lt_lapv%C3%A1ltozatok" title="Wikipédia:Jelölt lapváltozatok">közzétett változat</a>, <a class="external text" href="https://hu.wikipedia.org/w/index.php?title=Speci%C3%A1lis:Rendszernapl%C3%B3k&type=review&page=Fermi%E2%80%93Dirac-statisztika">ellenőrizve</a>: <i>2024. október 14.</i><p><table id="mw-fr-revisionratings-box" class="flaggedrevs-color-1" style="margin: auto;" cellpadding="0"><tr><td class="fr-text" style="vertical-align: middle;">Pontosság</td><td class="fr-value40" style="vertical-align: middle;">ellenőrzött</td></tr></table></p></div></div><div tabindex="0"></div></div></div></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="hu" dir="ltr"><p>A fizikában a <b>Fermi–Dirac-statisztika</b> (F–D-statisztika) leírja a részecskék energiaállapotát egy rendszerben, amely azonos részecskékből áll a <a href="/wiki/Pauli-elv" title="Pauli-elv">Pauli-elv</a> alapján. Az elnevezést <a href="/wiki/Enrico_Fermi" title="Enrico Fermi">Enrico Fermi</a> és <a href="/wiki/Paul_Dirac" title="Paul Dirac">Paul Dirac</a> fizikusokról kapták, akik egymástól függetlenül fedezték fel.<sup id="cite_ref-Fermi1926_1-0" class="reference"><a href="#cite_note-Fermi1926-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Dirac1926_2-0" class="reference"><a href="#cite_note-Dirac1926-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </p><p>Az F-D-statisztika termikus egyensúlyban lévő rendszerekben lévő félegész <a href="/wiki/Spin" title="Spin">spinnel</a> rendelkező részecskékre (<a href="/wiki/Fermionok" class="mw-redirect" title="Fermionok">fermionok</a>) vonatkozik. További feltételezés, hogy ezek a részecskék egymással elhanyagolható kölcsönhatásban vannak. Ez lehetővé teszi a sok részecskéből álló rendszerek leírását egyedi részecskék energiaállapotával. </p><p>A F-D-statisztika szerint két részecske nem lehet azonos állapotban, ez jelentős hatással van a rendszer tulajdonságaira. A leggyakrabban elektronokra alkalmazzák, melyek ½ spinnel rendelkező fermionok. Az F-D-statisztika része az általánosabb <a href="/wiki/Statisztikus_mechanika" title="Statisztikus mechanika">statisztikus mechanika</a> és a <a href="/wiki/Kvantummechanika" title="Kvantummechanika">kvantummechanika</a> elméletének. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Történet"><span id="T.C3.B6rt.C3.A9net"></span>Történet</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Fermi%E2%80%93Dirac-statisztika&action=edit&section=1" title="Szakasz szerkesztése: Történet"><span>szerkesztés</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Az F-D-statisztika 1926-ban történő bevezetése előtt nehéz volt megérteni néhány jelenséget az elektronokkal kapcsolatban, azok ellentmondásossága miatt. Például a fémek szobahőmérsékleten mért <a href="/wiki/H%C5%91kapacit%C3%A1s" title="Hőkapacitás">hőkapacitásánál</a> 100-szor kevesebb elektront tapasztaltak, mint az elektromos áramnál.<sup id="cite_ref-Kittel1971Cel249_3-0" class="reference"><a href="#cite_note-Kittel1971Cel249-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> </p><p>Azt is nehéz volt megérteni, hogy a fémekre ható nagyenergiájú tér hatására keletkező emissziós áram miért majdnem független a hőmérséklettől. Ezek a nehézségek abból adódtak, hogy 1926 előtt a klasszikus statisztikus elmélet szerint az elektronok mind egyformán viselkednek. Más szóval, azt hitték, hogy minden elektron a Boltzmann-állandó szerint járul hozzá a hőhöz. </p><p>Ez a statisztikai probléma megoldatlan maradt az F-D-statisztika felfedezéséig. </p><p>Az F-D-statisztikát először 1926-ban publikálta <a href="/wiki/Enrico_Fermi" title="Enrico Fermi">Enrico Fermi</a><sup id="cite_ref-Fermi1926_1-1" class="reference"><a href="#cite_note-Fermi1926-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> és <a href="/wiki/Paul_Dirac" title="Paul Dirac">Paul Dirac</a>.<sup id="cite_ref-Dirac1926_2-1" class="reference"><a href="#cite_note-Dirac1926-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </p><p><a href="/w/index.php?title=Pascual_Jordan&action=edit&redlink=1" class="new" title="Pascual Jordan (a lap nem létezik)">Pascual Jordan</a> hasonló elméletet fejlesztett ki 1925-ben, melyet Pauli-statisztikának nevezett el, de ezt nem publikálta időben.<sup id="cite_ref-Science-Week2000_4-0" class="reference"><a href="#cite_note-Science-Week2000-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p><p>Az F-D-statisztikát először 1926-ban <a href="/w/index.php?title=Raph_Fowler&action=edit&redlink=1" class="new" title="Raph Fowler (a lap nem létezik)">Raph Fowler</a> alkalmazta, amikor leírta egy csillag összeomlását fehér törpévé.<sup id="cite_ref-Fowler1926_5-0" class="reference"><a href="#cite_note-Fowler1926-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> </p><p><a href="/wiki/Arnold_Sommerfeld" title="Arnold Sommerfeld">Arnold Sommerfeld</a> az elektronokra alkalmazta az elméletet<sup id="cite_ref-sommerfeld1927_6-0" class="reference"><a href="#cite_note-sommerfeld1927-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> 1928-ban, Fowler és Nordheim az elektromos tér hatására történő <a href="/wiki/Elektronemisszi%C3%B3" title="Elektronemisszió">elektronemisszióra</a> alkalmazta az elméletet.<sup id="cite_ref-Fowler1928_7-0" class="reference"><a href="#cite_note-Fowler1928-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> A Fermi–Dirac-statisztika fontos részévé vált a fizikának. </p> <div class="mw-heading mw-heading2"><h2 id="Fermi–Dirac-eloszlás"><span id="Fermi.E2.80.93Dirac-eloszl.C3.A1s"></span>Fermi–Dirac-eloszlás</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Fermi%E2%80%93Dirac-statisztika&action=edit&section=2" title="Szakasz szerkesztése: Fermi–Dirac-eloszlás"><span>szerkesztés</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Az energiaszintek betöltöttségének valószínűségét a Fermi-Dirac-eloszlási függvény határozza meg. Azoknál a rendszereknél, melyek azonos fermionokat tartalmaznak, a fermionok számát a Fermi–Dirac-eloszlás adja meg:<sup id="cite_ref-Reif1965dist341_8-0" class="reference"><a href="#cite_note-Reif1965dist341-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> </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 {\bar {n}}_{i}={\frac {1}{e^{(\epsilon _{i}-\mu )/kT}+1}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>n</mi> <mo stretchy="false">¯</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <msub> <mi>ϵ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>−</mo> <mi>μ</mi> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>k</mi> <mi>T</mi> </mrow> </msup> <mo>+</mo> <mn>1</mn> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\bar {n}}_{i}={\frac {1}{e^{(\epsilon _{i}-\mu )/kT}+1}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dbdaa0058953d3db99712fc2daffbd26e1771726" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:19.125ex; height:5.676ex;" alt="{\displaystyle {\bar {n}}_{i}={\frac {1}{e^{(\epsilon _{i}-\mu )/kT}+1}}}"></span></dd></dl> <p>ahol <i>k</i> a <a href="/wiki/Boltzmann-%C3%A1lland%C3%B3" title="Boltzmann-állandó">Boltzmann-állandó</a>, <i>T</i> az abszolút hőmérséklet, <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 \epsilon _{i}\ }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ϵ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mtext> </mtext> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \epsilon _{i}\ }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2f872bab2767cb74592f25d64f9b91d0960574d2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.324ex; height:2.009ex;" alt="{\displaystyle \epsilon _{i}\ }"></span> egy <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle i}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>i</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle i}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/add78d8608ad86e54951b8c8bd6c8d8416533d20" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.802ex; height:2.176ex;" alt="{\displaystyle i}"></span> állapotú egyedi részecske energiája, és <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 \mu \ }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>μ</mi> <mtext> </mtext> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mu \ }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/99074b24941bae36892be9ed75f46020eebd33e4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.982ex; height:2.176ex;" alt="{\displaystyle \mu \ }"></span> a <a href="/wiki/K%C3%A9miai_potenci%C3%A1l" title="Kémiai potenciál">kémiai potenciál</a>. <i>T</i> = 0-nál a kémiai potenciál egyenlő a Fermi-energiával (Fermi-szint). Az F-D-eloszlás csak akkor érvényes a fermionok számának kiszámítására, ha a rendszer elég nagy, azaz egy plusz fermion hozzáadása elhanyagolható hatással van 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 \mu \ }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>μ</mi> <mtext> </mtext> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mu \ }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/99074b24941bae36892be9ed75f46020eebd33e4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.982ex; height:2.176ex;" alt="{\displaystyle \mu \ }"></span>-re.<sup id="cite_ref-Reif1965dist_9-0" class="reference"><a href="#cite_note-Reif1965dist-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> Mivel az F-D-eloszlás a Pauli-elvből származik, mely csak egy elektront enged meg minden egyes állapotban, az eredmény <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 0<{\bar {n}}_{i}<1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>0</mn> <mo><</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>n</mi> <mo stretchy="false">¯</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo><</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 0<{\bar {n}}_{i}<1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/558a9c69482dd7735a488bbc7be0b8afaa36717d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:10.716ex; height:2.509ex;" alt="{\displaystyle 0<{\bar {n}}_{i}<1}"></span>. </p><p>A <a href="/wiki/Sakk" title="Sakk">sakkjátékkal</a> történő összehasonlításban egy mezőben csak egy figura lehet, azaz a sakkfigurák átlagos száma négyzetenként nem lehet 1-nél nagyobb.) </p> <div class="mw-heading mw-heading3"><h3 id="Fermi-szint">Fermi-szint</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Fermi%E2%80%93Dirac-statisztika&action=edit&section=3" title="Szakasz szerkesztése: Fermi-szint"><span>szerkesztés</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Félvezetőkben lévő elektronoknál 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 \mu \ }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>μ</mi> <mtext> </mtext> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mu \ }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/99074b24941bae36892be9ed75f46020eebd33e4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.982ex; height:2.176ex;" alt="{\displaystyle \mu \ }"></span> -t Fermi-szintnek is hívják.<sup id="cite_ref-Blakemore2002p11_10-0" class="reference"><a href="#cite_note-Blakemore2002p11-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-KittelKroemer1980_11-0" class="reference"><a href="#cite_note-KittelKroemer1980-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> A Fermi-szint az az energiaérték, ahol az elektronnal és lyukkal való betöltöttség valószínűsége megegyezik. A vezetőkben a Fermi-szint a vezetési sávban (lásd energiasávok), a szigetelőkben a vegyértéksávban van, félvezetők esetében pedig a vezetési sáv és a vegyértéksáv közé esik. Az abszolút nulla hőmérsékleten az elektronok betöltik az energiaszinteket a Fermi-szintig, de a magasabb szintek nincsenek betöltve. Az intrinsic félvezető Fermi-szintje gyakorlatilag a tiltott sáv közepén helyezkedik el. N típusú félvezetőben a Fermi-szint a tiltott sáv felső felében, p típusú félvezetőben a tiltott sáv alsó felében helyezkedik el. Az adalékolás növelésével a Fermi-szint a sávszélek felé mozdul el, a hőmérséklet növekedésével fordítva, a sáv közepe felé mozdul. </p> <figure class="mw-halign-center" typeof="mw:File/Thumb"><a href="/wiki/F%C3%A1jl:FD_e_mu.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c9/FD_e_mu.svg/300px-FD_e_mu.svg.png" decoding="async" width="300" height="299" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c9/FD_e_mu.svg/450px-FD_e_mu.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c9/FD_e_mu.svg/600px-FD_e_mu.svg.png 2x" data-file-width="354" data-file-height="353" /></a><figcaption>F-D eloszlás, energia függés</figcaption></figure> <figure class="mw-halign-center" typeof="mw:File/Thumb"><a href="/wiki/F%C3%A1jl:FD_kT_e.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/5e/FD_kT_e.svg/300px-FD_kT_e.svg.png" decoding="async" width="300" height="304" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/5e/FD_kT_e.svg/450px-FD_kT_e.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/5e/FD_kT_e.svg/600px-FD_kT_e.svg.png 2x" data-file-width="358" data-file-height="363" /></a><figcaption>F-D eloszlás, hőmérséklet függés</figcaption></figure> <div class="mw-heading mw-heading2"><h2 id="Jegyzetek">Jegyzetek</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Fermi%E2%80%93Dirac-statisztika&action=edit&section=4" title="Szakasz szerkesztése: Jegyzetek"><span>szerkesztés</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="ref-1col"><div style="-moz-column-count:2; -webkit-column-count:2; column-count:2; -webkit-column-gap: 3em; -moz-column-gap: 3em; column-gap: 3em;"><ol class="references"> <li id="cite_note-Fermi1926-1"><span class="mw-cite-backlink">↑ <a href="#cite_ref-Fermi1926_1-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Fermi1926_1-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><cite class="book citation" style="font-style:normal" id="Reference-Fermi-1926">Fermi, Enrico (1926). „Sulla quantizzazione del gas perfetto monoatomico” (olasz nyelven). <i>Rend. Lincei</i> <b>3</b>, 145–9. o.</cite><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Sulla+quantizzazione+del+gas+perfetto+monoatomico&rft.jtitle=Rend.+Lincei&rft.date=1926&rft.volume=3&rft.aulast=Fermi&rft.aufirst=Enrico&rft.pages=145%E2%80%939"><span style="display:none"> </span></span>, translated as <cite class="book citation" style="font-style:normal"> (1999. december 14.) „On the Quantization of the Monoatomic Ideal Gas”.</cite><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=On+the+Quantization+of+the+Monoatomic+Ideal+Gas&rft.date=1999-12-14"><span style="display:none"> </span></span></span> </li> <li id="cite_note-Dirac1926-2"><span class="mw-cite-backlink">↑ <a href="#cite_ref-Dirac1926_2-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Dirac1926_2-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><cite class="book citation" style="font-style:normal" id="Reference-Dirac-1926"><a href="/wiki/Paul_Dirac" title="Paul Dirac">Dirac, Paul A. M.</a> (1926). „On the Theory of Quantum Mechanics”. <i>Proceedings of the Royal Society, Series A</i> <b>112</b> (762), 661–77. o. <a href="/wiki/Digital_object_identifier" title="Digital object identifier">DOI</a>:<a rel="nofollow" class="external text" href="https://dx.doi.org/10.1098/rspa.1926.0133">10.1098/rspa.1926.0133</a>. <a href="/wiki/JSTOR" title="JSTOR">JSTOR</a> <a rel="nofollow" class="external text" href="https://www.jstor.org/stable/94692">94692</a>.</cite><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=On+the+Theory+of+Quantum+Mechanics&rft.jtitle=Proceedings+of+the+Royal+Society%2C+Series+A&rft.date=1926&rft.volume=112&rft.issue=762&rft.aulast=Dirac&rft.aufirst=Paul+A.+M.&rft.pages=661%E2%80%9377&rft_id=info:doi/10.1098%2Frspa.1926.0133"><span style="display:none"> </span></span></span> </li> <li id="cite_note-Kittel1971Cel249-3"><span class="mw-cite-backlink"><a href="#cite_ref-Kittel1971Cel249_3-0">↑</a></span> <span class="reference-text">(<a href="#CITEREFKittel1971">Kittel 1971</a>, pp. 249–50)</span> </li> <li id="cite_note-Science-Week2000-4"><span class="mw-cite-backlink"><a href="#cite_ref-Science-Week2000_4-0">↑</a></span> <span class="reference-text"><cite class="book citation" style="font-style:normal"> (2000. május 19.) „<a rel="nofollow" class="external text" href="https://web.archive.org/web/20090411105016/http://scienceweek.com/2000/sw000519.htm#">History of Science: The Puzzle of the Bohr–Heisenberg Copenhagen Meeting</a>”. <i><a href="/w/index.php?title=ScienceWeek&action=edit&redlink=1" class="new" title="ScienceWeek (a lap nem létezik)">Science-Week</a></i>, Chicago <b>4</b> (20). [2009. április 11-i dátummal az <a rel="nofollow" class="external text" href="http://scienceweek.com/2000/sw000519.htm">eredetiből</a> archiválva]. (Hozzáférés: 2009. január 20.)</cite><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=History+of+Science%3A+The+Puzzle+of+the+Bohr%E2%80%93Heisenberg+Copenhagen+Meeting&rft.jtitle=%5B%5BScienceWeek%7CScience-Week%5D%5D&rft.date=2000-05-19&rft.volume=4&rft.issue=20&rft_id=http%3A%2F%2Fscienceweek.com%2F2000%2Fsw000519.htm"><span style="display:none"> </span></span></span> </li> <li id="cite_note-Fowler1926-5"><span class="mw-cite-backlink"><a href="#cite_ref-Fowler1926_5-0">↑</a></span> <span class="reference-text"><cite class="book citation" style="font-style:normal" id="Reference-Fowler-1926"><a href="/wiki/Ralph_Fowler" title="Ralph Fowler">Fowler, Ralph H.</a> (1926. December). „On dense matter”. <i>Monthly Notices of the Royal Astronomical Society</i> <b>87</b>, 114–22. o.</cite><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=On+dense+matter&rft.jtitle=Monthly+Notices+of+the+Royal+Astronomical+Society&rft.date=1926&rft.volume=87&rft.aulast=Fowler&rft.aufirst=Ralph+H.&rft.pages=114%E2%80%9322"><span style="display:none"> </span></span></span> </li> <li id="cite_note-sommerfeld1927-6"><span class="mw-cite-backlink"><a href="#cite_ref-sommerfeld1927_6-0">↑</a></span> <span class="reference-text"><cite class="book citation" style="font-style:normal"><a href="/wiki/Arnold_Sommerfeld" title="Arnold Sommerfeld">Sommerfeld, Arnold</a> (1927. október 14.). „Zur Elektronentheorie der Metalle”. <i><a href="/w/index.php?title=Naturwissenschaften&action=edit&redlink=1" class="new" title="Naturwissenschaften (a lap nem létezik)">Naturwissenschaften</a></i> <b>15</b> (41), 824–32. o. <a href="/wiki/Digital_object_identifier" title="Digital object identifier">DOI</a>:<a rel="nofollow" class="external text" href="https://dx.doi.org/10.1007/BF01505083">10.1007/BF01505083</a>. (Hozzáférés: 2009. január 18.)</cite><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Zur+Elektronentheorie+der+Metalle&rft.jtitle=%5B%5BNaturwissenschaften%5D%5D&rft.date=1927-10-14&rft.volume=15&rft.issue=41&rft.aulast=Sommerfeld&rft.aufirst=Arnold&rft.pages=824%E2%80%9332&rft_id=info:doi/10.1007%2FBF01505083"><span style="display:none"> </span></span></span> </li> <li id="cite_note-Fowler1928-7"><span class="mw-cite-backlink"><a href="#cite_ref-Fowler1928_7-0">↑</a></span> <span class="reference-text"><cite class="book citation" style="font-style:normal">Fowler, Ralph H. (1928. május 1.). „<a rel="nofollow" class="external text" href="http://rspa.royalsocietypublishing.org/content/119/781/173.full.pdf">Electron Emission in Intense Electric Fields</a>” (PDF). <i>Proceedings of the Royal Society A</i> <b>119</b> (781), 173–81. o. <a href="/wiki/Digital_object_identifier" title="Digital object identifier">DOI</a>:<a rel="nofollow" class="external text" href="https://dx.doi.org/10.1098/rspa.1928.0091">10.1098/rspa.1928.0091</a>. <a href="/wiki/JSTOR" title="JSTOR">JSTOR</a> <a rel="nofollow" class="external text" href="https://www.jstor.org/stable/95023">95023</a>.</cite><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Electron+Emission+in+Intense+Electric+Fields&rft.jtitle=Proceedings+of+the+Royal+Society+A&rft.date=1928-05-01&rft.volume=119&rft.issue=781&rft.aulast=Fowler&rft.aufirst=Ralph+H.&rft.pages=173%E2%80%9381&rft_id=info:doi/10.1098%2Frspa.1928.0091&rft_id=http%3A%2F%2Frspa.royalsocietypublishing.org%2Fcontent%2F119%2F781%2F173.full.pdf"><span style="display:none"> </span></span></span> </li> <li id="cite_note-Reif1965dist341-8"><span class="mw-cite-backlink"><a href="#cite_ref-Reif1965dist341_8-0">↑</a></span> <span class="reference-text">(<a href="#CITEREFReif1965">Reif 1965</a>, p. 341)</span> </li> <li id="cite_note-Reif1965dist-9"><span class="mw-cite-backlink"><a href="#cite_ref-Reif1965dist_9-0">↑</a></span> <span class="reference-text">(<a href="#CITEREFReif1965">Reif 1965</a>, pp. 340–2)</span> </li> <li id="cite_note-Blakemore2002p11-10"><span class="mw-cite-backlink"><a href="#cite_ref-Blakemore2002p11_10-0">↑</a></span> <span class="reference-text">(<a href="#CITEREFBlakemore2002">Blakemore 2002</a>, p. 11)</span> </li> <li id="cite_note-KittelKroemer1980-11"><span class="mw-cite-backlink"><a href="#cite_ref-KittelKroemer1980_11-0">↑</a></span> <span class="reference-text"><cite class="book citation" style="font-style:normal" id="Reference-Kittel-1980"><a href="/w/index.php?title=Charles_Kittel&action=edit&redlink=1" class="new" title="Charles Kittel (a lap nem létezik)">Kittel, Charles</a>. <i><a rel="nofollow" class="external text" href="https://books.google.com/?id=c0R79nyOoNMC&pg=PA357">Thermal Physics</a></i>, 2nd, San Francisco: W. H. Freeman, 357. o. (1980). <a href="/wiki/Speci%C3%A1lis:K%C3%B6nyvforr%C3%A1sok/978-0716710882" title="Speciális:Könyvforrások/978-0716710882">ISBN 978-0716710882</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=Thermal+Physics&rft.aulast=Kittel&rft.aufirst=Charles&rft.date=1980&rft.edition=2nd&rft.pub=W.+H.+Freeman&rft.place=San+Francisco&rft.pages=357&rft.isbn=978-0716710882&rft_id=https%3A%2F%2Fbooks.google.com%2F%3Fid%3Dc0R79nyOoNMC%26pg%3DPA357"><span style="display: none;"> </span></span></span> </li> </ol></div></div><div class="ref-1col"><div style="-moz-column-count:2; -webkit-column-count:2; column-count:2; -webkit-column-gap: 3em; -moz-column-gap: 3em; column-gap: 3em;"></div></div> <div class="mw-heading mw-heading2"><h2 id="További_információk"><span id="Tov.C3.A1bbi_inform.C3.A1ci.C3.B3k"></span>További információk</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Fermi%E2%80%93Dirac-statisztika&action=edit&section=5" title="Szakasz szerkesztése: További információk"><span>szerkesztés</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>Pintér Ferenc: <i>Általános fizika, Atomhéjfizika).</i> (hely nélkül): Dialóg Campus Kiadó. 2003.  569–575. o. <small><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fhu.wikipedia.org%3AFermi%E2%80%93Dirac-statisztika&rft.au=Pint%C3%A9r+Ferenc&rft.btitle=%C3%81ltal%C3%A1nos+fizika%2C+Atomh%C3%A9jfizika%29&rft.date=2003&rft.genre=book&rft.pages=569%E2%80%93575&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988"><span style="display:none;"> </span></span></small></li> <li><a rel="nofollow" class="external free" href="http://www.bmf.hu/users/grollerg/Villamosiparianyagismeret/prezentaciok/07Villamos-tul.pdf">http://www.bmf.hu/users/grollerg/Villamosiparianyagismeret/prezentaciok/07Villamos-tul.pdf</a><sup class="noprint Inline-Template"><span style="white-space: nowrap;">[<i><a rel="nofollow" class="external text" href="https://web.archive.org/web/*/http://www.bmf.hu/users/grollerg/Villamosiparianyagismeret/prezentaciok/07Villamos-tul.pdf"><span title="  2018-11">halott link</span></a></i>]</span></sup></li> <li><a rel="nofollow" class="external free" href="http://www.vilaglex.hu/Fizika/Html/FermiSzi.htm">http://www.vilaglex.hu/Fizika/Html/FermiSzi.htm</a></li> <li><a rel="nofollow" class="external free" href="http://www.jegyzet.hu/uploaded/474/02_-_elektro2.pdf">http://www.jegyzet.hu/uploaded/474/02_-_elektro2.pdf</a><sup class="noprint Inline-Template"><span style="white-space: nowrap;">[<i><a rel="nofollow" class="external text" href="https://web.archive.org/web/*/http://www.jegyzet.hu/uploaded/474/02_-_elektro2.pdf"><span title="  2018-11">halott link</span></a></i>]</span></sup></li> <li><a rel="nofollow" class="external free" href="http://hyperphysics.phy-astr.gsu.edu/hbase/solids/fermi.html">http://hyperphysics.phy-astr.gsu.edu/hbase/solids/fermi.html</a></li> <li><a rel="nofollow" class="external free" href="http://kando.prociweb.hu/letoltes/data/3.evfolyam/EE_Alkatresz/Mikroelektronika%20%E9s%20f%E9lvezet%F5%20%E1ramk%F6r%F6k%20tervez%E9se/MikroTerv4SzilardtFiz2.pdf">http://kando.prociweb.hu/letoltes/data/3.evfolyam/EE_Alkatresz/Mikroelektronika%20%E9s%20f%E9lvezet%F5%20%E1ramk%F6r%F6k%20tervez%E9se/MikroTerv4SzilardtFiz2.pdf</a><sup class="noprint Inline-Template"><span style="white-space: nowrap;">[<i><a rel="nofollow" class="external text" href="https://web.archive.org/web/*/http://kando.prociweb.hu/letoltes/data/3.evfolyam/EE_Alkatresz/Mikroelektronika%20%E9s%20f%E9lvezet%F5%20%E1ramk%F6r%F6k%20tervez%E9se/MikroTerv4SzilardtFiz2.pdf"><span title="  2018-11">halott link</span></a></i>]</span></sup></li></ul></div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1&useformat=desktop" alt="" width="1" height="1" style="border: none; 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