量子力学中的数学概念

图书标准信息

• 作者 [加拿大]格斯特松 著
• 出版社 世界图书出版公司
• 出版时间 2009-08
• 版次 1
• ISBN 9787510005022
• 定价 35.00元
• 装帧 平装
• 开本 24开
• 纸张 胶版纸
• 页数 286页
• 正文语种 英语
• 原版书名 Mathematical Concepts of Quantum Mechanics

【内容简介】

　　Thefirstfifteenchaptersoftheselectures（omittingfourtosixchapterseachyear）coveraonetermcoursetakenbyamixedgroupofseniorundergraduateandjuniorgraduatestudentsspecializingeitherinmathematicsorphysics.Typically，themathematicsstudentshavesomebackgroundinadvancedanalysis，whilethephysicsstudentshavehadintroductoryquantummechanics.Tosatisfysuchadisparateaudience，wedecidedtoselectmaterialwhichisinterestingfromtheviewpointofmoderntheoreticalphysics，andwhichillustratesaninterplayofideasfromvariousfieldsofmathematicssuchasoperatortheory，probability，differentialequations，anddifferentialgeometry.Givenourtimeconstraint，wehaveoftenpursuedmathematicalcontentattheexpenseofrigor.However，whereverwehavesacrificedthelatter，wehavetriedtoexplainwhethertheresultisanestablishedfact，or，mathematicallyspeaking，aconjecture，andintheformercase，howagivenargumentcanbemaderigorous.Thepresentbookretainsthesefeatures.

【目录】

1PhysicalBackground
1.1TheDouble-SlitExperiment
1.2WaveFunctions
1.3StateSpace
1.4TheSchr6dingerEquation
1.5MathematicalSupplement：OperatorsonHilbertSpaces，

2Dynamics
2.1ConservationofProbability
2.2ExistenceofDynamics
2.3TheFreePropagator
2.4MathematicalSupplement：OperatorAdjoints
2.5MathematicalSupplement：theFourierTransform
2.5.1DefinitionoftheFourierTransform
2.5.2PropertiesoftheFourierTransform
2.5.3FunctionsoftheDerivative

3Observables
3，1MeanValuesandtheMomentumOperator
3.2Observables
3.3TheHeisenbergRepresentation
3.4Quantization
3.5PseudodifferentialOperators

4TheUncertaintyPrinciple
4.1TheHeisenbergUncertaintyPrinciple
4.2ARefinedUncertaintyPrinciple
4.3Application：StabilityofHydrogen
5SpectralTheory
5.1TheSpectrumofanOperator
5.2FunctionsofOperatorsandtheSpectralMappingTheorem..
5.3ApplicationstoSchrodingerOperators
5.4SpectrumandEvolution
5.5VariationalCharacterizationofEigenvalues
5.6NumberofBoundStates
5.7MathematicalSupplement：IntegralOperators

6ScatteringStates
6.1Short-raageInteractions：μ>1
6.2Long-rangeInteractions：μ<1
6.3WaveOperators

7SpecialCases
7.1TheInfiniteWell
7.2TheTorns
7.3APotentialStep
7.4TheSquareWell
7.5TheHarmonicOscillator
7.6AParticleonaSphere
7.7TheHydrogenAtom
7.8AParticleinanExternalEMField

8Many-particleSystems
8.1QuantizationofaMany-particleSystem
8.2SeparationoftheCentre-of-massMotion
8.3Break-ups
8.4TheHVZTheorem
8.5Intra-vs.Inter-clusterMotion
8.6ExistenceofBoundStatesforAtomsandMolecules
8.7ScatteringStates
8.8MathematicalSupplement：TensorProducts
8.9Appendix：HartreeandGross-PitaevskiEquations

9DensityMatrices
9.1Introduction
9.2StatesandDynamics
9.3OpenSystems
9.4TheThermodynamicLimit
9.5EquilibriumStates
9.6TheT→OLimit
9.7Example：aSystemofHarmonicOscillators
9.8AParticleCoupledtoaReservoir
9.9QuantumSystems
9.10Problems
9.11HilbertSpaceApproach
9.12BECatT=O
9.13Appendix：theIdealBoseGas
9.14Appendix：Beee-EinsteinCondensation
9.15MathematicalSupplement：theTrace，andTraceClassOperators
9.16MathematicalSupplement：Projections

10PerturbationTheory：FeshbachMethod
10.1TheFeshbachMethod
10.2Example：TheZeemanEffect
10.3Example：Time-dependentPerturbations
10.4Appendix：ProofofTheorem10.1

11TheEeynmanPathIntegral....
11.1TheFeynmanPathIntegral
11.2GeneralizationsofthePathIntegral
11.3MathematicalSupplement：TheTrotterProductFormula

12Quasi-classicalAnalysis
12.1Quasi-classicalAsymptotiesofthePropagator
12.2Quasi-classicalAsymptoticsofGreensFunction
12.2.1Appendix
12.3Bohr-SommerfeldSemi-classicalQuantization
12.4Quasi-classicalAsymptoticsfortheGroundStateEnergy
12.5MathematicalSupplement：OperatorDeterminants

13MathematicalSupplement：TheCalculusofVariations.
13.1Functionals
13.2TheFirstVariationandCriticalPoints
13.3ConstrainedVariationalProblems
13.4TheSecondVariation
13.5ConjugatePointsandJacobiFields
13.6TheActionoftheCriticalPath
13.7Appendix：ConnectiontoGeodesics

14Resonances
14.1TunnelingandResonances
14.2TheFreeResonanceEnergy
14.3Instantons
14.4PositiveTemperatures
14.5Pre-exponentialFactorfortheBounce
14.6ContributionoftheZero-mode
14.7Bohr-SommerfeldQuantizationforResonances

15IntroductiontoQuantumFieldTheory
15.1ThePlaceofQFT
15.1.1PhysicalTheories
15.1.2ThePrincipleofMinimalAction
15.2Klein-GordonTheoryasaHamiltoulanSystem
15.2.1TheLegendreTransform
15.2.2Hamiltoninns
15.2.3PoisonBrackets
15.2.4HamiltonsEquations
15.3MaxwellsEquationsasaHamiltonianSystem
15.4QuantizationoftheKlein-GordonandMaxwellEquations..
15.4.1TheQuantizationProcedure
15.4.2CreationandAnnihilationOperators
15.4.3WickOrdering
15.4.4QuantizingMaxwallsEquations
15.5FockSpace
15.6GeneralizedFreeTheory
15.7Interactions
15.8QuadraticApproximation
15.8.1FurtherDiscussion
15.8.2ABriefRemarkonMany-bodyHamiltoniansinSecondQuantizationandtheHartreeApproximation.

16QuantumElectrodynamicsofNon-relatlvisticParticles：TheTheoryofRadiation
16.1TheHamiltonian
16.2PerturbationSet-up
16.3Results
16.4MathematicalSupplements
16.4.1SpectralProjections
16.4.2Projecting-outProcedure

17Supplement：RenormalizationGroup
17.1TheDecimationMap
17.2RelativeBounds
17.3EliminationofParticleandHighPhotonEnergyDegreesofFreedom
17.4GeneralizedNormalFormofOperatorsonFockSpace
17.5TheHamiltonianH0(ε，z)
17.6ABanachSpaceofOperators
17.7Rescaling
17.8TheRenormalizationMap
17.9LinearizedFlow
17.10Central-stableManifoldforRGandSpectraofHamiltonians
17.11Appendix

18CommentsonMissingTopics，Literatnre，andFurtherReading
References
Index