quantum mechanics - concepts and applications

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

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

3、1.2Theinnerproduct................................21.3Linearoperators.................................51.4Eigenstatesandeigenvalues...........................61.5TheDiracdeltafunction.............................132TheLaws(Postulates)ofQuantumMechanics162.1Alessonfromclassicalmechani

4、cs........................162.2Thepostulatesofquantummechanics.....................172.3Somehistoryofthepostulates.........................193PopularRepresentations203.1Thepositionrepresentation...........................203.2Themomentumrepresentation.........................234SomeS

5、impleExamples254.1TheHamiltonian,conservedquantitiesandexpectationvalue........254.2Freeparticleinonedimension..........................304.2.1Momentum................................31ii4.2.2Energy...................................314.2.3Position..................................32

6、4.3Theharmonicoscillator.............................344.3.1Solutioninpositionrepresentation...................364.3.2Arepresentationfreesolution......................394.4Landaulevels...................................425MoreOneDimensionalExamples455.1Generalcharacteristicsofsolutio

7、ns.......................455.1.1E

8、.....555.2.2