《原子分子與光子理論》課程教學(xué)大綱

ADDINCNKISM.UserStyle《原子分子與光子理論》課程教學(xué)大綱中文課程簡介（含課程名、課程編號、學(xué)分、總學(xué)時(shí)、課程內(nèi)容概要等內(nèi)容）課程名：原子分子與光子理論課程編號：0702061003學(xué)分：2總學(xué)時(shí)：32《原子分子與光子理論》課程是為物理學(xué)博士研究生開設(shè)的選修課。只有研究清楚了物質(zhì)的基本組成單位——原子或分子等微觀結(jié)構(gòu)的性質(zhì)，才能對物質(zhì)的相變以及與輻射的相互作用有詳細(xì)的了解。這一知識使物質(zhì)特性的進(jìn)一步可控優(yōu)化成為可能。因此，原子分子光子物理學(xué)不僅是一個(gè)重要的基礎(chǔ)研究領(lǐng)域，而且許多應(yīng)用本質(zhì)上構(gòu)成我們現(xiàn)在技術(shù)世界。理解材料及其在日常生活中的應(yīng)用，對我們的文化以及我們對自然環(huán)境的態(tài)度有重大影響。本課程目的是介紹微觀世界的原子，分子和光子的特點(diǎn)。它闡述了我們對物質(zhì)微觀結(jié)構(gòu)的認(rèn)識以及輻射是如何產(chǎn)生的，同時(shí)介紹了哪些關(guān)鍵的實(shí)驗(yàn)迫使現(xiàn)有的經(jīng)典理論得到擴(kuò)展和改進(jìn)，最終發(fā)展成了原子和分子物理的基礎(chǔ)理論——量子理論。理論只有聯(lián)系實(shí)際，才能更好地理解它。第1章給出了量子理論最簡單真實(shí)的系統(tǒng)即氫原子系統(tǒng)。這里再次說明，為了理解所有的實(shí)驗(yàn)結(jié)果，實(shí)驗(yàn)強(qiáng)制將量子力學(xué)擴(kuò)展到量子電動力學(xué)。第2章討論了具有多電子的較大原子的描述，這也將化學(xué)元素的化學(xué)性質(zhì)歸結(jié)為電子殼層的結(jié)構(gòu)的影響，并解釋了為什么所有元素都可以排列在周期表中。第3章討論了物質(zhì)與輻射相互作用這一重要課題。這為第4章討論的激光的解釋奠定了基礎(chǔ)。分子，由兩個(gè)及兩個(gè)以上的原子構(gòu)成，是組成我們多樣性世界的一個(gè)重要基礎(chǔ)。它們將在第5章講述。特別是關(guān)于原子怎樣形成穩(wěn)定分子，以及發(fā)生哪種相互作用的，進(jìn)行了更詳細(xì)的論述。在第6章中，給出了探究原子和分子的多種實(shí)驗(yàn)技術(shù)；最后一章7章簡要概述了原子和分子物理學(xué)的最新發(fā)展，說明物理學(xué)永遠(yuǎn)不會是一個(gè)完整的、最終確定的領(lǐng)域。還有很多有待探索的地方，仍然需要新的想法和廣泛的科學(xué)熱情，來推動我們知識的進(jìn)一步發(fā)展。二、英文課程簡介（含課程名、課程編號、學(xué)分、總學(xué)時(shí)、課程內(nèi)容概要等內(nèi)容）CourseName：《Atom,MoleculeandPhoton》CourseNumber：0702061003Credit:2Semestertotalhours:32Thedetailedunderstandingofmatter,itsphasetransitionsanditsinteractionwithradiationcouldbeonlyreached,afteritsmicroscopicstructuredeterminedbythekindofatomsormoleculesasbasicconstituentsofmatterhadbeeninvestigated.Thisknowledgeallowedthecontrolledoptimizationofcharacteristicpropertiesofmatter.Atomicphysicsthereforerepresentsnotonlyanareaofimportantfundamentalresearch,buthasfurthermoremanyapplicationswhichhaveessentiallyformedourpresenttechnicalworld.Theunderstandingofmaterialsandtheiruseindailylife,hasmajorimpactofourcultureandourattitudetowardsnatureandourenvironment.Thistextbookisaimedasanintroductiontothemicroscopicworldofatoms,moleculesandphotons.Itillustrateshowourknowledgeaboutthemicroscopicstructureofmatterandradiationcameaboutandwhichcrucialexperimentsforcedanextensionandrefinementofexistingclassicaltheories,culminatinginthedevelopmentofquantumtheory,whichisnowacceptedasthebasictheoryofatomicandmolecularphysics.Atheorycanbebestunderstoodbyapplicationstoarealsituation.InChap.1thequantumtheoryofthesimplestrealsystem,namelythehydrogenatom,ispresented.Hereitisagainillustrated,thatexperimentsenforcedanextensionofquantummechanicstoquantumelectrodynamicsinordertounderstandallexperimentalresults.ThedescriptionoflargeratomswithmanyelectronsistreatedinChap.2,whichalsoreducesthechemicalpropertiesofchemicalelementstothestructureoftheelectronshellsandexplainswhyallelementscanbearrangedinaperiodictable.TheimportantsubjectofinteractionofmatterwithradiationisdiscussedinChap.3.Thispreparesthegroundfortheexplanationoflasers,treatedinChap.4.Molecules,consistingoftwoormoreatoms,formthebasisforthegreatvarietyofourworld.TheyarediscussedinChaps.5.Inparticularthequestion,whyandhowatomscanformstablemolecules,andwhichkindofinteractionoccurs,istreatedinmoredetail.InChap.6thedifferentexperimentaltechniquesfortheinvestigationofatomsandmoleculesarepresented,inordertogivethereaderafeelingfortheinventiveideasandthenecessaryexperimentalskillfortheirrealization.Thelastchapter.7presentsashortoverviewonrecentdevelopmentsinatomicandmolecularphysics,whichshalldemonstratethatphysicswillbeneveracompleteandfinalizedfield.Thereisstillmuchtoexploreandnewideasandscientificenthusiasmisneeded,topushtheborderofourknowledgefurtherahead.教學(xué)目標(biāo)通過《原子分子與光子》課程的學(xué)習(xí)，使學(xué)生樹立原子分子光子的基本概念，掌握原子分子及光子物理學(xué)的基本規(guī)律，了解其實(shí)驗(yàn)和理論研究思想和方法，了解原子與分子及光子物理學(xué)的發(fā)展現(xiàn)狀及基本應(yīng)用。Throughthestudyofthecourse“Atoms,MoleculesandPhotons”,studentscansetupthebasicconceptsofatomicandmolecularphotons,masterthebasiclawsofatomicandmolecularandphotonphysics,understandtheideasandmethodsofexperimentalandtheoreticalresearch,andunderstandthedevelopmentstatusandbasicapplicationsofatomicandmolecularandphotonphysics.教學(xué)內(nèi)容Contents（目錄）Basedonpreviousstudiesofquantummechanics,wewillnowapplythequantummechanicaltreatmenttothesimplestatom,theHatom,whichconsistsofoneprotonandone-electronmovinginthesphericalsymmetricCoulombpotentialoftheproton.Theseone-electronsystems,suchasthehydrogenatomandtheionsHe+,Li++,Be+++,etc.,aretheonlyrealsystemsforwhichtheSchr?dingerequationcanbeexactly(i.e.,analytically)solved.Forallotheratomsormoleculesapproximationshavetobemade.EithertheSchr?dingerequationforthesesystemscanbesolvednumerically(whichofferamathematicalsolutionwithintheaccuracyofthecomputerprogram,butgenerallygiveslittleinsightintothephysicalnatureoftheapproximation),ortherealatomsaredescribedbyapproximatemodelsthatcanbecalculatedanalytically.Inanycase,forallmultielectronsystems,onehastolivewithapproximations,eitherinthenumericalsolutionoftheexactatomicmodelorfortheexactsolutionoftheapproximatemodel.Acloserinspectionofthespectrumofthehydrogenatomandotheratomsreveals,however,thatathigherspectralresolutionthelinesshowasubstructurethatcannotbedescribedbytheSchr?dingertheory,butisduetoneweffects,suchasfinestructure,hyperfinestructureortheanomalousZeemaneffect.Therefore,evenforthesimplehydrogenatomthequantummechanicalmodelofanelectronintheCoulombfieldoftheprotonhastobemodifiedbyintroducingnewpropertiesofelectronandproton,suchaselectronspinorprotonspinandtheirmutualinteractions.Theseeffects,whicharesmallcomparedtotheCoulombenergy,areincludedinarelativistictheory,basedontheDiracequation,whichiscalledquantumelectrodynamics.TheSchr?-dingerequationcanberegardedasthefundamentalequationofnonrelativisticquantumtheory.Thetreatmentofthehydrogenatomillustratesinaveryclearwaythebasicideasofquantummechanics,itexplainsthephysicalinterpretationofquantumnumbers,thedescriptionoftheZeemaneffectandthefinestructurebythemodelofangularmomentumvectorcouplingsandgivesabetterunderstandingofthemorecomplexmany-electronsystems.基于之前所學(xué)的量子力學(xué)的，我們現(xiàn)在將量子力學(xué)應(yīng)用于由一個(gè)質(zhì)子和一個(gè)在質(zhì)子的球?qū)ΨQ庫侖勢中運(yùn)動的電子組成的最簡單原子——H原子。如氫原子和離子He+，L++，Be+++等單電子系統(tǒng)，是薛定諤方程唯一可以精確(即解析)求解的真實(shí)系統(tǒng)。對于所有其他的原子或分子，必須進(jìn)行近似。這些系統(tǒng)的薛定諤方程可以用數(shù)值方法求解(這提供了計(jì)算機(jī)程序精度范圍內(nèi)的數(shù)學(xué)解，但通常很少給出近似的物理本質(zhì))，或者真實(shí)原子由可以解析計(jì)算的近似模型描述。在任何情況下，對于所有的多電子系統(tǒng)，無論是精確原子模型的數(shù)值解還是近似模型的精確解，我們都須進(jìn)行近似。然而，對氫原子和其他原子的光譜進(jìn)行更仔細(xì)的觀察發(fā)現(xiàn)，在更高的光譜分辨率下，這些線顯示出一種無法用Schr?dinger理論描述的子結(jié)構(gòu)，但這是由于新的效應(yīng)，如精細(xì)結(jié)構(gòu)、超精細(xì)結(jié)構(gòu)或反常塞曼效應(yīng)。因此，即使對于簡單的氫原子，電子在質(zhì)子庫侖場中的量子力學(xué)模型也必須通過引入電子和質(zhì)子的新性質(zhì)來修改，如電子自旋或質(zhì)子自旋及其相互作用。這些與庫侖能量相比較小的效應(yīng)包含在相對論理論中，該理論基于狄拉克方程，稱為量子電動力學(xué)。薛定諤方程可以視為非相對論量子理論的基本方程。氫原子的處理以一種非常清晰的方式闡明了量子力學(xué)的基本思想，它解釋了量子數(shù)的物理解釋，用角動量矢量耦合模型描述塞曼效應(yīng)和精細(xì)結(jié)構(gòu)，使我們更好地理解更復(fù)雜的多電子系統(tǒng)。2.AtomswithMoreThanOneElectron（多于一個(gè)電子的原子）Inatomswithmorethanoneelectronadditionalproblemsarisethatarecausedbymutualelectrostaticandmagneticinteractionsbetweentheelectrons.Inaddition,wearenowconfrontedwithnewsymmetryprinciplesthatarevalidiftwoelectronsareexchanged.Thesestemfromthefactthatelectronscannotbedistinguishedfromeachother.Wewillfirststudythesephenomenafortheheliumatom,whichrepresentsthesimplestsystemwithtwoelectrons.Thiswillhelpusunderstandthebuildingupprincipleforthestructureofelectronshellsforlargeratoms.Wewillseethattheelectronconfigurationsforallatomscanbeobtainedfromtheminimumenergyprinciple,thecorrectcouplingofthedifferentangularmomentaoftheelectronsandtheobservationofcertainsymmetryrules.Thisresultsinthedeterminationofallpossibleenergystatesoftheatomsandthecharacterizationofthesestatesbyquantumnumbers.在有多個(gè)電子的原子中，電子之間的相互靜電和磁性相互作用會引起額外的問題。此外，我們現(xiàn)在面臨的新對稱原理是有效的如果兩個(gè)電子交換。這是由于電子不能彼此區(qū)別的事實(shí)。我們將首先研究氦原子的這些現(xiàn)象，它代表了具有兩個(gè)電子的最簡單系統(tǒng)。這將有助于我們理解大原子的電子層結(jié)構(gòu)的建立原理。我們將看到所有原子的電子構(gòu)型可以從最小能量原理，電子的不同角動量的正確耦合和某些對稱規(guī)則的觀察得到。這結(jié)果在決定所有可能的能量狀態(tài)的原子和表征這些狀態(tài)的量子數(shù)。3.EmissionandAbsorptionofElectromagneticRadiationbyAtoms（原子對電磁輻射的發(fā)射和吸收）WementionedthatatomscanundergotransitionsbetweendifferentstateswithenergiesEiandEk,whenaphotonwithenergy?ω=Ek-Eiisemittedorabsorbed.Experimentsshow,however,thattheabsorptionoremissionspectrumofanatomdoesnotcontainallpossiblefrequenciesω.Theremustbecertain“selectionrules”thatselectfromallpossiblecombinationsEiandEkonlythosebetweenwhicharadiativetransitioncantakeplace.Furthermore,theintensityofthespectrallinescanvarybymanyordersofmagnitude,whichmeansthattheprobabilityofatransitiongenerallydependsstronglyonthespecificcombinationofthetwoatomicstates.Besidestheenergyconservationalsothetotalangularmomentumofthesystem(atom+photon)hastobeconserved.Thetransitionprobabilitythereforedependsonthepolarizationoftheemittedorabsorbedelectromagneticradiation.Inthischapterwewilldiscusshowsuchtransitionprobabilitiescanbecalculatedfromthewavefunctionsofthestatesinvolvedinthetransition當(dāng)吸收或釋放一個(gè)具有能量?ω=Ek-Ei的光子時(shí)，原子可以在能量為Ei和Ek的不同狀態(tài)之間發(fā)生躍遷.而，實(shí)驗(yàn)表明，一個(gè)原子的吸收或發(fā)射光譜并不包含所有可能的頻率ω。必須有一定的“選擇定則”，從所有可能的組合Ei和Ek中選擇可以發(fā)生輻射躍遷的組合。此外，譜線的強(qiáng)度可以變化許多數(shù)量級，這意味著躍遷的概率通常強(qiáng)烈依賴于兩個(gè)原子狀態(tài)的特定組合。4.DiatomicMolecules（雙原子分子）Wewilldiscussthebasicphysicsofmolecules.Inparticular,thefollowingquestionsshallbeaddressedandanswered:Whycanneutralatomscombinetoformstablemolecules,i.e.,whatisthenatureofmolecularbindingforces?Whatistheinternalenergystructureofmolecules,whichnotonlydependsonthedistributionofelectronsinatoms,butalsoonthelocationandmotionofatomicnuclei?Howcanchemicalreactions,andthereforebiologicalprocesses,beexplainedonamolecularlevel?Firstwewilldiscussdiatomicmolecules,becausetheirtreatmentissimplerthanthatofpolyatomicmolecules.Fromthedidacticalpointofview,theyprovideagoodunderstandingofmanyproblems,whicharerelevantnotonlytodiatomicsbutalsotopolyatomicmolecules.Inparticular,theinteractionbetweentwoneutralatomsanditsdependenceontheirdistanceRfromeachotherwillgiveusbetterinsightintothenatureofchemicalbonds.Also,themodelofatomicorbitals,whichgiveanintuitivepictureofthespatialelectrondistributionandplayanimportantroleinchemistry,canbeexplainedmorereadilyfordiatomicmolecules.Similarlytothesituationforatoms,transitionsbetweendifferentmolecularlevelscanbeinducedbyabsorptionoremissionofradiation.Sincetheenergylevelsofmoleculesarenotonlydeterminedbyelectronicexcitationbutalsobyvibrationsofthenucleiortherotationofthewholemoleculearoundanaxisthroughitscenterofmass,thespectraofmoleculesaremuchmorecomplexthanthoseofatoms,butontheotherhandtheyalsogivemoredetailedinformationabouttheinternalstructureanddynamicsofmolecules.Wewilldiscussthespectraofdiatomicmolecules。Wewillstartwiththesimplifiedmodelofrigidmolecules,wherethenucleiareclampedatagivenposition.Fordiatomicmoleculesthismeansthattheinternucleardistanceisfixedandweneglecttheirvibration.Foranyarbitrary,butconstant,valueofRtheenergyofthemoleculeiscalculated.ThisyieldsthepotentialenergycurvesE(R)forthedifferentelectronicstatesofthemolecule.Lateronwewillthenextendourmodeltoinclude