Search Back to top Filter ResultsLocationBookshelves (1)ClassificationArticle typeBook or UnitChapterSection or PageN/AN/AAuthorJeremy TatumLloyd KnoxOpenStaxBen CrowellMichael FowlerPaul D'AlessandrisMalcolm McMillianJeffrey W. SchnickDina ZhabinskayaChris ImpeyDouglas ClinePaul SeeburgerTom WeidemanNiels WaletDavid HarrisonBoundlessRichard FitzpatrickFred Jendrzejewski, Selim Jochim, & Matthias WeidemüllerTimon IdemaLawrence DavisDaniel ArovasDaniel F. StyerRyan Martin et al.UCD Physics 7 sans DinaJulio Gea-BanaclocheJohn F. Cochran and Bretislav HeinrichDaniel E. BarthLei MaSteven W. EllingsonMichael RichmondDavid H. StaelinJohan WeversPeter DourmashkinKyle Forinash and Wolfgang ChristianJack C. StratonGraeme AcklandPaola CappellaroKim Coble, Kevin McLin, Janelle Bailey, Anne Metevier, Carolyn Peruta, & Lynn CominskyLászló TiszaWolfgang Christian, Mario Belloni, Anne Cox, Melissa H. Dancy, and Aaron Titus, & Thomas M. ColbertDavid J. RaymondV. Parameswaran NairHoward GeorgiY. D. ChongKonstantin K. LikharevEvan HalsteadWalter FendtMihály BenedictPieter KokSander Konijnenberg, Aurèle J.L. Adam, & H. Paul UrbachEdwin F. Taylor & John Archibald WheelerJames M. FioreRob KnopRyan D. Martin, Emma Neary, Joshua Rinaldo, and Olivia WoodmanRonald KumonLumen LearningDebra Fischer, Allyson Sheffield, Joshua Tan, and Lily Ling ZhaoEmbed Hypothes.is?yesEmbebbed CalcPlot3D?yesCover PageyesTOC OnlyCompile but don't publishLicensePublic DomainCC BYCC BY-SACC BY-NC-SACC BY-NDCC BY-NC-NDGNU GPLAll Rights ReservedCC BY-NCGNU FDLShow TOCyesnoTranscludedyesOER program or PublisherCollege of the Canyons - Zero Textbook Cost ProgramASCCC OERI ProgramCK-12OpenStaxGALILEOOpenSUNYMIT OpenCourseWareVirginia Tech Libraries' Open Education InitiativeThe Publisher Who Must Not Be NamedeCampusOntarioWAC ClearinghouseBC CampusLumenOpen OregonOpenStax CNXPDXOpenEvergreen Valley CollegeStudent AnalyticsyesAutonumber Section Headingstitle with space delimiterstitle with colon delimiterstitle with dash delimitersLicense Version1.02.02.53.04.0Print CSSScreen CSSdefaultVirginia TechCosmologyPrintOptionsNo Header/FooterNo TitleNo Header/Footer/TitleInclude attachmentsContent TypeDocumentImageOther Searching inAll resultsAbout 1 results5.1: Statistical Mechanics of Noninteracting Quantum Systemshttps://phys.libretexts.org/Bookshelves/Thermodynamics_and_Statistical_Mechanics/Book%3A_Thermodynamics_and_Statistical_Mechanics_(Arovas)/05%3A_Noninteracting_Quantum_Systems/5.01%3A_Statistical_Mechanics_of_Noninteracting_Quantum_Systems\[\begin{split} Z\ns_N&=\sum_{\{n\ns_\alpha\}}\,e^{-\beta\sum_\alpha n\ns_\alpha \ve\ns_\alpha}\,\delta\ns_{N,\sum_\alpha n\ns_\alpha}\\ &=\sum_{\alpha\ns_1}\sum_{\alpha\ns_2}\>\cdots\>\sum_{\alpha\ns...\[\begin{split} Z\ns_N&=\sum_{\{n\ns_\alpha\}}\,e^{-\beta\sum_\alpha n\ns_\alpha \ve\ns_\alpha}\,\delta\ns_{N,\sum_\alpha n\ns_\alpha}\\ &=\sum_{\alpha\ns_1}\sum_{\alpha\ns_2}\>\cdots\>\sum_{\alpha\ns_N}\left({\prod_\alpha n\ns_\alpha!\over N!}\right)\> e^{-\beta(\ve_{\alpha\ns_1}+\ \ve_{\alpha\ns_2} + \ \ldots\ +\ \ve_{\alpha\ns_N})}\ . \end{split}\]MoreShow more results
