浙江大学大学物理甲下-chapter-47.ppt

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1、Chapter47ElectronsinPotentialWells1Whatisquantummechanics?Quantummechanicsislawofthemicrocosm,especiallyislawthathowthemembersofthemicrocosmmakeupintothemacrocosm.Quantummechanicsislawdescribingthemotionofparticleswhichwithlowerenergy,especiallythemotionofelectr

2、ons.247-1Electrons,FreeandBoundTheprincipaldifferencebetweenafreeandaboundelectronisAboundelectronsislocalized.itsenergyisquantized.Energyofafreeelectronisnotquantized.347-2AnElectronTrappedinaPotentialwellAccordingtoNewtonianmechanics,theelectroncanonlybounceba

3、ckandforthinthecentralregionbetweenturningpointsatx=–L/2andx=+L/2ifitsenergyElessthanU0.4Howevertheelectron’sactualbehaviorisnotdescribedbyNewtonianmechanicsbutbyquantummechanics.Aninfinitelydeeppotentialwell51.SolveSchrödingerequationoutsidethewellthesolutionis

4、6insidethewellLwhereThegeneralsolutionis7ThegeneralsolutionisBytheboundaryconditions：Thewavefunctionis:Probabilitydensity8insidethewellwhereThegeneralsolutionis9Bytheboundaryconditions：Thegeneralsolutionis1011whenwhenProbabilitydensity122.Energylevelsforaninfini

5、tewellTheenergyisquantized.Thequantummechanicalresultrestrictsthevaluesofenergy.13LocalizationleadstoquantizationWecalltheinteger“n”aquantumnumber.14153.Probabilitydensitiesforaninfinitewell16Theprobabilitydistributionofanelectronisdifferentwithx.17Atincreasingl

6、yhighquantumnumbers,thepredictionsofquantummechanicsmergesmoothlywiththoseofNewtonianmechanics,thatistheprobabilityoffindinganelectroninthewellisthesameeverywhere.18Whennislarge,therearenodifferencesbetweenψoddandψeven.194.NormalizationForoddwavefunctionand,fore

7、venwavefunction205.ZeropointenergyThegroundstateisthestateforn=1,andthecorrespondingenergyisthelowestlevel,whichisTheenergieshigherthanthegroundstateenergyarecalledexcitedstateenergies.Zeropointenergy21QuickQuiz-1Anelectronistrappedinaninfiniteone-dimensionalpot

8、entialwellofwidthL.(a)Whatistheminimumpossibleenergyoftheelectron?(1)0;(2)between0andh2/8mL2;(3)～h2/8mL2,butitisnotpossibletofindtheexactvaluebecauseoftheuncertaintyp