quantum mechanics - a modern development - l. ballentine

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1、ThisPageIntentionallyLeftBlankContentsPrefacexiIntroduction:ThePhenomenaofQuantumMechanics1Chapter1MathematicalPrerequisites71.1LinearVectorSpace71.2LinearOperators111.3Self-AdjointOperators151.4HilbertSpaceandRiggedHilbertSpace261.5ProbabilityTheory29Problem

2、s38Chapter2TheFormulationofQuantumMechanics422.1BasicTheoreticalConcepts422.2ConditionsonOperators482.3GeneralStatesandPureStates502.4ProbabilityDistributions55Problems60Chapter3KinematicsandDynamics633.1TransformationsofStatesandObservables633.2TheSymmetries

3、ofSpace–Time663.3GeneratorsoftheGalileiGroup683.4IdentificationofOperatorswithDynamicalVariables763.5CompositeSystems853.6[[QuantizingaClassicalSystem]]873.7EquationsofMotion893.8SymmetriesandConservationLaws92Problems94Chapter4CoordinateRepresentationandAppli

4、cations974.1CoordinateRepresentation974.2TheWaveEquationandItsInterpretation984.3GalileiTransformationofSchr¨odinger’sEquation102vviContents4.4ProbabilityFlux1044.5ConditionsonWaveFunctions1064.6EnergyEigenfunctionsforFreeParticles1094.7Tunneling1104.8PathInt

5、egrals116Problems123Chapter5MomentumRepresentationandApplications1265.1MomentumRepresentation1265.2MomentumDistributioninanAtom1285.3Bloch’sTheorem1315.4DiffractionScattering:Theory1335.5DiffractionScattering:Experiment1395.6MotioninaUniformForceField145Problem

6、s149Chapter6TheHarmonicOscillator1516.1AlgebraicSolution1516.2SolutioninCoordinateRepresentation1546.3SolutioninHRepresentation157Problems158Chapter7AngularMomentum1607.1EigenvaluesandMatrixElements1607.2ExplicitFormoftheAngularMomentumOperators1647.3OrbitalA

7、ngularMomentum1667.4Spin1717.5FiniteRotations1757.6RotationThrough2π1827.7AdditionofAngularMomenta1857.8IrreducibleTensorOperators1937.9RotationalMotionofaRigidBody200Problems203Chapter8StatePreparationandDetermination2068.1StatePreparation2068.2StateDetermin

8、ation2108.3StatesofCompositeSystems2168.4IndeterminacyRelations223Problems227ContentsviiChapter9MeasurementandtheInterpretationofStates2309.1AnExampleofSpinMeasurement2309.2AGeneralTheore