quantum mechanics for undergraduates

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1、QUANTUMMECHANICSProfessorJohnW.NorburyPhysicsDepartmentUniversityofWisconsin-MilwaukeeP.O.Box413Milwaukee,WI53201November20,2000Contents1WAVEFUNCTION71.1ProbabilityTheory........................81.1.1Mean,Average,ExpectationValue...........81.1.2AverageofaFunction..................101.1.3Mean,Median

2、,Mode..................101.1.4StandardDeviationandUncertainty..........111.1.5ProbabilityDensity...................141.2PostulatesofQuantumMechanics...............141.3ConservationofProbability(ContinuityEquation)......191.3.1ConservationofCharge.................191.3.2ConservationofProbability.....

3、..........221.4InterpretationoftheWaveFunction..............231.5ExpectationValueinQuantumMechanics...........241.6Operators.............................241.7CommutationRelations.....................271.8Problems.............................321.9Answers..............................332DIFFERENTIALEQ

4、UATIONS352.1OrdinaryDi®erentialEquations.................352.1.1SecondOrder,Homogeneous,Linear,OrdinaryDi®er-entialEquationswithConstantCoe±cients......362.1.2InhomogeneousEquation................392.2PartialDi®erentialEquations..................422.3PropertiesofSeparableSolutions................442

5、.3.1GeneralSolutions.....................442.3.2StationaryStates.....................442.3.3De¯niteTotalEnergy..................4512CONTENTS2.3.4AlternatingParity....................462.3.5Nodes...........................462.3.6CompleteOrthonormalSetsofFunctions.......462.3.7Time-dependentCoe±cients

6、..............492.4Problems.............................502.5Answers..............................513INFINITE1-DIMENSIONALBOX533.1EnergyLevels...........................543.2WaveFunction..........................573.3Problems.............................633.4Answers..............................644P

7、OSTULATESOFQUANTUMMECHANICS654.1MathematicalPreliminaries...................654.1.1HermitianOperators...................654.1.2EigenvalueEquations..................664.2Postulate4.....................