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1、QuantummechanicsandquantumstructuresPurposeofthismoduleThismoduleisnotaquantummechanicscourse.Insteadthemoduleisintendedtodiscusssomespecificaspectsofquantummechanics.Itishopedthatthisdiscussionwillallowstudentstoimprovetheirintuitiveunderstandingofquantummechanics.©E.F.Schubert,RensselaerPolytec
2、hnicInstitute,20031ThebirthofquantummechanicsIn1900MaxPlanckcorrectlydescribedthespectralpowerdensityofablack-bodyradiatorbyassumingthequantizedoscillationstatesofatomsofthebody.(afterUniversityCorporationforAtmosphericResearch)©E.F.Schubert,RensselaerPolytechnicInstitute,20032Planck(1900)postula
3、tedthattheoscillatingatomsofablackbodyradiateenergyonlyinthediscrete,i.e.quantizedamounts2π2π2πE=hω,2hω,3hωL=hc,2hc,3hcLλλλwhereħ=h/(2π)isPlanck’sconstantdividedby2π,cisthevelocityoflight,andω=2πfistheintrinsicangularfrequencyoftheradiatingoscillators.ThequantumconstantorPlanck’sconstanthasavalue
4、of−34h=h/2π=1.05×10Js.Employingthispostulateintheblack-bodyradiationproblem,PlanckobtainedthefollowingformulaforthespectralintensitydistributionofablackbodyattemperatureT2⎡5⎛⎛2πhc⎞⎞⎤I(λ)=4πhc⎢λ⎜⎜exp⎜⎜⎟⎟–1⎟⎟⎥⎢⎣⎝⎝λkT⎠⎠⎥⎦©E.F.Schubert,RensselaerPolytechnicInstitute,20033ClassicalparticleinwellExampl
5、e:GolfballinwellAssumption:Nofriction©E.F.Schubert,RensselaerPolytechnicInstitute,20034Questions:Whydowemaketheassumptionofnofriction?Whatare“classicalturningpoints”?Showtheprobabilitydensityfunctionoftheparticle!Discussthefollowingpotentialwell:©E.F.Schubert,RensselaerPolytechnicInstitute,20035W
6、hatisanelectron?Particlesandwaveshaveverydifferentproperties.However,itisnecessarytoinvokebothnatures,toexplaindifferentphenomenaassociatedwithelectrons.©E.F.Schubert,RensselaerPolytechnicInstitute,20036Illustrativeexample:Thedouble-slitexperimentToexplainallaspectsofthedouble-slitexperiment,both
7、naturesoftheelectronneedtobeinvoked.©E.F.Schubert,RensselaerPolytechnicInstitute,20037Theintensitydistributiononthescreenisexplainedbythewavenatureofelectrons,namelybyinterferenceeffects.However,onecanremovethescreenan
