quantum mechanics - concepts and applications

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1、QuantumMechanics{ConceptsandApplicationsTarunBiswasJune16,1999CopyrightCopyright°c1990,1994,1995,1998,1999byTarunBiswas,PhysicsDepartment,StateUniversityofNewYorkatNewPaltz,NewPaltz,NewYork12561.CopyrightAgreementThisonlineversionofthebookmaybereproducedfreelyinsmallnumbers(10orlessperindi

2、vidual)aslongasitisdoneinitsentiretyincludingthetitle,theauthor'snameandthiscopyrightpage.Forlargernumbersofcopiesonemustobtaintheauthor'swrittenconsent.Copiesofthisbookmaynotbesoldforpro¯t.iContents1MathematicalPreliminaries11.1Thestatevectors.................................11.2Theinnerp

3、roduct................................21.3Linearoperators.................................51.4Eigenstatesandeigenvalues...........................61.5TheDiracdeltafunction.............................132TheLaws(Postulates)ofQuantumMechanics162.1Alessonfromclassicalmechanics................

4、........162.2Thepostulatesofquantummechanics.....................172.3Somehistoryofthepostulates.........................193PopularRepresentations203.1Thepositionrepresentation...........................203.2Themomentumrepresentation.........................234SomeSimpleExamples254.1TheHam

5、iltonian,conservedquantitiesandexpectationvalue........254.2Freeparticleinonedimension..........................304.2.1Momentum................................31ii4.2.2Energy...................................314.2.3Position..................................324.3Theharmonicoscillator......

6、.......................344.3.1Solutioninpositionrepresentation...................364.3.2Arepresentationfreesolution......................394.4Landaulevels...................................425MoreOneDimensionalExamples455.1Generalcharacteristicsofsolutions.......................455.1.1E

7、x)forallx............................465.1.2Boundstates...............................475.1.3Scatteringstates.............................495.2Someoversimpli¯edexamples..........................535.2.1Rectangularpotentialwell(boundstates)...............555.2.2