量子力学原理

1.MathematicalIntroduction

1.1.LinearVectorSpaces：Basics

1.2.InnerProductSpaces

1.3.DualSpacesandtheDiracNotation

1.4.Subspaces

1.5.LinearOperators

1.6.MatrixElementsofLinearOperators

1.7.ActiveandPassiveTransformations

1.8.TheEigenvalueProblem

1.9.FunctionsofOperatorsandRelatedConcepts

1.10.GeneralizationtoInfiniteDimensions

2.ReviewofClassicalMechanics

2.1.ThePrincipleofLeastActionandLagrangianMechanics

2.2.TheElectromagneticLagrangian

2.3.TheTwo-BodyProblem

2.4.HowSmartIsaParticle?

2.5.TheHamiltonianFormalism

2.6.TheElectromagneticForceintheHamiltonianScheme

2.7.CyclicCoordinates,PoissonBrackets，andCanonicalTransformations

2.8.SymmetriesandTheirConsequences.

3.AllIsNotWellwithClassicalMechanics

3.1.ParticlesandWavesinClassicalPhysics

3.2.AnExperimentwithWavesandParticles(Classical)

3.3.TheDouble.SlitExperimentwithLight

3.4.MatterWaves(deBroglieWaves)

3.5.Conclusions

4.ThePostulates-aGeneralDiscussion

4.1.ThePostulates

4.2.DiscussionofPostulatesI-III

4.3.TheSchr6dingerEquation(DottingYourisandCrossingyourhs)

5.SimpleProblemsinOneDimension

5.1.TheFreeParticle

5.2.TheParticleinaBox

5.3.TheContinuityEquationforProbability

5.4.TheSingle-StepPotential：aProbleminScattering

5.5.TheDouble-SlitExperiment

5.6.SomeTheorems

6.TheClassicalLimit

7.TheHarmonicOscillator

7.1.WhyStudytheHarmonicOscillator?

7.2.ReviewoftheClassicalOscillator

7.3.QuantizationoftheOscillator(CoordinateBasis)

7.4.TheOscillatorintheEnergyBasis

7.5.PassagefromtheEnergyBasistotheXBasis

8.ThePathIntegralFormulationofQuantumTheory

8.1.ThePathIntegralRecipe

8.2.AnalysisoftheRecipe

8.3.AnApproximationtoU(t)fortheFreeParticle

8.4.PathIntegralEvaluationoftheFree.ParticlePropagator

8.5.EquivalencetotheSchr6dingerEquation

8.6.PotentialsoftheFormV=a+bx+cx2+dx+exx

9.TheHeisenbergUncertaintyRelations

9.1.Introduction

9.2.DerivationoftheUncertaintyRelations

9.3.TheMinimumUncertaintyPacket

9.4.ApplicationsoftheUncertaintyPrinciple

9.5.TheEnergy-TimeUncertaintyRelation

10.SystemswithNDegreesofFreedom

10.1.NParticlesinOneDimension

10.2.MoreParticlesinMoreDimensions

10.3.IdenticalParticles

11.SymmetriesandTheirConsequences

11.1.Overview

11.2.TranslationalInvarianceinQuantumTheory

11.3.TimeTranslationalInvariance

11.4.ParityInvariance

11.5.Time.ReversalSymmetry

12.RotationalInvarianeeandAngularMomentum

12.1.TranslationsinTwoDimensions

12.2.RotationsinTwoDimensions

12.3.TheEigenvalueProblemofLz

12.4.AngularMomentuminThreeDimensions

12.5.TheEigenvalueProblemofL2andLz

12.6.SolutionofRotationallyInvariantProblems

13.TheHydrogenAtom

13.1.TheEigenvalueProblem

13.2.TheDegeneracyoftheHydrogenSpectrum

13.3.NumericalEstimatesandComparisonwithExperiment

13.4.MultielectronAtomsandthePeriodicTable

14.Spin

14.1.Introduction

14.2.WhatiStheNatureofSpin?

14.3.KinematicsofSpin

14.4.SpinDynamics

14.5.ReturnOfOrbitalDegreesofFreedom

15.AdditionofAngularMomenta

15.1.ASimpleExample

15.2.TheGeneralProblem

15.3.IrreducibleTensor0perators

15.4.ExplanationofSome“Accidental”Degeneracies

16.VariationalandWKBMethods

16.1.TheVariationalMethod.

16.2.TheWentzel-Kramers-BrillouinMethod

17.Time-IndependentPerturbationTheory

17.1.TheFormalism

17.2.SomeExamples

17.3.DegeneratePerturbationTheory

18.Time-DependentPerturbationTheory

18.1.TheProblem.

18.2.First-OrderPerturbationTheory

18.3.HigherOrdersinPerturbationTheory

18.4.AGeneralDiscussionofElectromagneticInteractions

18.5.InteractionofAtomswithElectromagneticRadiation

19.ScatteringTheory

19.1.Introduction

19.2.RecapitulationofOne-DimensionalScatteringandOverview

19.3.TheBornApproximation(Time-DependentDescription)

19.4.BornAgain(TheTime-IndependentApproximation)

19.5.ThePartialWaveExpansion

19.6.Two-ParticleScattering

20.TheDiracEquation

20.1.TheFree-ParticleDiracEquation

20.2.ElectromagneticInteractionoftheDiracParticle

20.3.MoreonRelativisticQuantumMechanics

21.PathIntegrals-II

21.1.DerivationofthePathIntegral

21.2.ImaginaryTimeFormalism

21.3.SpinandFermionPathIntegrals

21.4.Summary

Appendix

A.1.MatrixInversion

A.2.GaussianIntegrals

A.3.ComplexNumbers

A.4.TheiεPrescription

ANSWERSTOSELECTEDEXERCISES

TABLEOFCONSTANTS

INDEX

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