量子力学对称性

1.SymmetriesinQuantumMechanics

1.1SymmetriesinClassicalPhysics

1.2SpatialTranslationsinQuantumMechanics

1.3TheUnitaryTranslationOperator

1.4TheEquationofMotionforStatesShiftedinSpace

1.5SymmetryandDegeneracyofStates

1.6TimeDisplacementsinQuantumMechanics

1.7MathematicalSupplement:DefinitionofaGroup

1.8MathematicalSupplement:RotationsandtheirGroupTheoreticalProperties

1.9AnIsomorphismoftheRotationGroup

1.10TheRotationOperatorforMany-ParticleStates

1.11BiographicalNotes

2.AngularMomentumAlgebraRepresentationofAngularMomentumOperators:GeneratorsofSO(3)

2.1IrreducibleRepresentationsoftheRotationGroup

2.2MatrixRepresentationsofAngularMomentumOperators

2.3AdditionofTwoAngularMomenta

2.4EvaluationofClebsch-GordanCoefficients

2.5RecursionRelationsforClebsch-GordanCoefficients

2.6ExplicitCalculationofClebsch-GordanCoefficients

2.7BiographicalNotes

3.MathematicalSupplement:FundamentalPropertiesofLieGroups

3.1GeneralStructureofLieGroups

3.2InterpretationofCommutatorsasGeneralizedVectorProducts,LiesTheorem,RankofLieGroup

3.3InvariantSubgroups,SimpleandSemisimpleLieGroups,Ideals

3.4CompactLieGroupsandLieAlgebras

3.5InvariantOperators(CasimirOperators)

3.6TheoremofRacah

3.7CommentsonMultiplets

3.8InvarianceUnderaSymmetryGroup

3.9ConstructionoftheInvariantOperators

3.10RemarkonCasimirOperatorsofAbelianLieGroups

3.11CompletenessRelationforCasimirOperators

3.12ReviewofSomeGroupsandTheirPropertiesandTransformationsofFunctions

3.14BiographicalNotes

4.SymmetryGroupsandTheirPhysicalMeaning:GeneralConsiderations

4.1BiographicalNotes

5.ThelsospinGroup(IsobaricSpin)

5.1IsospinOperatorsforaMulti-NucleonSystem

5.2GeneralPropertiesofRepresentationsofaLieAlgebra

5.3Regular(orAdjoint)RepresentationofaLieAlgebra

5.4TransformationLawforIsospinVectors

5.5ExperimentalTestofIsospinlnva

7.5CouplingofT,UandVMultiplets

7.6QuantitativeAnalysisofOurReasoning

7.7FurtherRemarksAbouttheGeometricFormofanSU(3)Multiplet

7.8TheNumberofStatesonMeshPointsonInnerShells

8.QuarksandSU(3)

8.1SearchingforQuarks

8.2TheTransformationPropertiesofQuarkStates

8.3ConstructionofallSU(3)MultipletsfromtheElementaryRepresentations(3)and

8.4ConstructionoftheRepresentationD(p,q)fromQuarksandAntiquarks

8.5MesonMultiplets

8.6RulesfortheReductionofDirectProductsofSU(3)Multiplets

8.7U-SpinInvariance

8.8TestofU-SpinInvariance

……

9.RepresentationsofthePermutationGroupandYoungTableanx

10.MathematicalExcursionGroupCharacters

11.CharmandSU(4)

12.MathematicalSupplement

13.SpecialDiscrdtsSymmetries

14.DynamicalSymmetries

15.MathematicalExcursion:Non-compactLieGruoups

16.ProffofRacahsTheorem

SubjectIndex

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