e-book_-_john_norbury_-_quantum_mechanics_for_undergraduates

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

2、Function..................101.1.3Mean,Median,Mode..................101.1.4StandardDeviationandUncertainty..........111.1.5ProbabilityDensity...................141.2PostulatesofQuantumMechanics...............141.3ConservationofProbability(ContinuityEquation

3、)......191.3.1ConservationofCharge.................191.3.2ConservationofProbability...............221.4InterpretationoftheWaveFunction..............231.5ExpectationValueinQuantumMechanics...........241.6Operators.............................241.7Commutatio

4、nRelations.....................271.8Problems.............................321.9Answers..............................332DIFFERENTIALEQUATIONS352.1OrdinaryDi®erentialEquations.................352.1.1SecondOrder,Homogeneous,Linear,OrdinaryDi®er-entialEquations

5、withConstantCoe±cients......362.1.2InhomogeneousEquation................392.2PartialDi®erentialEquations..................422.3PropertiesofSeparableSolutions................442.3.1GeneralSolutions.....................442.3.2StationaryStates................

6、.....442.3.3De¯niteTotalEnergy..................4512CONTENTS2.3.4AlternatingParity....................462.3.5Nodes...........................462.3.6CompleteOrthonormalSetsofFunctions.......462.3.7Time-dependentCoe±cients..............492.4Problems.........

7、....................502.5Answers..............................513INFINITE1-DIMENSIONALBOX533.1EnergyLevels...........................543.2WaveFunction..........................573.3Problems.............................633.4Answers..........................

8、....644POSTULATESOFQUANTUMMECHANICS654.1MathematicalPreliminaries...................654.1.1HermitianOperators...................654.1.2EigenvalueEquations..................664.2Postulate4.....................