M40_KNIG7655_03_ITG_CH40

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1、CHAPTER40One-DimensionalQuantumMechanicsRecommendedclassdays:3BackgroundInformationAtthispoint,studentshaveseenthat:•Atomicparticlesexhibitwave-likebehavior.•StandingdeBrogliewavesleadtoquantizationofenergy.•TheBohrmodelsuggeststhatrealatomshavequantizedenergylevels.•Wave-particledual

2、itycanbeunderstoodwithaprobabilisticwavefunction.Nowweneedtoassemblethesebitsandpiecesintoanactualtheoryofmatterontheatomicscale.Thegoalsofthischapterarequitelimited.Physicsmajorsandthoseengineerswhomightusequantummechanicsextensivelywillgoontotakeamodernphysicscourseandperhapsafullco

3、urseinquantummechanics.Forthem,thischapterisanintroduction.Alargergroupofstudentsneedstounderstandthesignificanceofenergylevelsandwavefunctions,particularlyastheyapplytoissuessuchasmolecularbondsortunneling,butthey’llneverhavetosolvetheSchrödingerequationforthemselves.Hencethefocusoft

4、hischapterison:•Modelingquantumsystems.•InterpretingandusingsolutionsoftheSchrödingerequation.•Understandingquantumphenomenasuchastunneling.Thesegoalscanbemetwithone-dimensionalquantummechanicsasappliedtotime-independent,bound-stateproblemswithreal-valuedsolutions.Studentsarenotexpect

5、edoraskedtosolvedifferentialequations,buttheyshouldlearntorecognizeandinterpretthemajorfeaturesofasolutionoftheSchrödingerequation.Classicalmechanicsanalyzesphenomenabydevelopingamodeloftheforcesactingonaparticle.Someforcesmaybeaccuratelyknown,othersarereasonableapproximations.Oncethe

6、40-1forcesofthemodelareidentified,theparticle’strajectorycanbefoundbysolvingNewton’ssecondlaw.Wealsousemodelsinquantummechanics,butnowthemodelsareexpressedintermsofapotentialenergyfunction.Thisismuchharderforstudentstodealwith.AlthoughpotentialenergydiagramswereemphasizedinChapter10,m

7、oststudentswillneedtoreviewhowpotentialenergydiagramsareinterpretedclassicallytoyieldturningpoints,kineticenergies,forces,andsoon.Youwillalsoneedtobeveryexplicitwithyourexplanationsofhowaparticleconfinedtoacertainregioncanbemodeledasbeinginapotentialenergywell.UnpublishedresearchatKan

8、sasSt