非相对论量子力学基础
2000-6
世界图书出版公司
L.Sobrino
332
It is almost a trivial observation that many collective endeavours require the accomplishment of numerous complicated tasks, and that the different individuals that perform them may lose sight of the overall design. Like other creative endeavours, the scientific quest is particularly prone to such a state of affairs, for not only does the difficulty of the tasks absorb the mind but the beauty of what is learnt in performing them engages the soul. Like a diver, who may be so charmed by the nearby coral so as to forget that its beauty is but a minute reflection of the majestic beauty of the ocean, a spectroscopist may be so taken by the beautiful symmetries that the molecules exhibit so as to loose sight of the wonderful structure of quantum mechanics that informs them. ...
PREFACE.I.INTRODUCTION1.Descriptionofexperiments2.Theconceptofphysicalsystem3.PreparationandmeasurementII.STATESANDOBSERVABLES1.Statesandamplitudes2.Anexample:spin1/23.Observables4.ThedensityoperatorIII.COMMENSURABILITY 1.Thespinexamplecontinued 2.Differentkindsofmeasurement 3.Commensurableobservables 4.TheuncertaintyrelationIV.DYNAMICS 1.Thcdynamicalpostulate 2.Schrodinger,Helsenbergandmixedpictures 3.Anasideonfunctionsofseveralobservables 4.Thehamiltonian 5.Equationsofmotioninthedifferentpictures 6.AnexampleV.GENERALFORMULATION 1.Generalizationofthebasicpostulates 2.Dirac'sformulation 3.Kinematicalsymmetries 4.Thedynamicsunderakinematicalsymmetry 5.Thegalileantransformationsaskinematicalsymmetries 6.Thegeneratorsofkinematicalgalileantransformations 7.SuperselectionrulesVI.APARTICLEINONEDIMENSION 1.Aparticlewithoutspin 2.Themomentumoperator 3.Thevelocity,themassandthehamiltonian 4.Anexample:theharmonicoscillator 5.AparticleinaconstantforcefieldVII.ASPINLESSPARTICLEINTHREEDIMENSIONS 1.Position,momentumandthehamiltonian 2.Rotations,theorbitalangularmomentum 3.Theangularmomentumcommutationrelations 4.Spectralresolutionoftheorbitalangularmomentum 5.Thefreeparticle 6.TheWignerdistributionfunction 7.Theharmonicoscillator 8.Thespinlessparticleinageneralcoordinatesystem 9.TheparticleinacentralfieldVIII.DYNAMICALSYMMETRIESANDCONSERVATIONLAWS 1.Thedynamicalsymmetrytransformationsofquantummechanics.. 2.Unitarytransformationsandconstantsofthemotion 3.Spaceinversion,theparityobservable 4.Timereversal 5.ThegalileantransformationsasdynamicalsymmetriesIX.APARTICLEWITHSPIN 1.Internaldegreesoffreedomandgalileaninvariance 2.Spinandrotations 3.Theparticlewithspin 4.Tilehamiltonianofaparticlewithspin 5.Example:aneutralparticleinamagneticfieldX.SYSTEMSCOMPOSEDOFDIFFERENTSUBSYSTEMS 1.Thedescriptionofsystemsformedbydifferentsubsystems 2.Asystemoftwodifferentparticles 3.Someusefulrepresentations 4.Thestateofasubsystem 5.Example:statesofaparticleinamagneticfieldXI.SYSTEMSOFIDENTICALPARTICLES 1.Thedescriptionofsystemsformedbytwoidenticalsubsystems 2.Example:asystemoftwoidenticalparticles 3.Thedescriptionofsystemsofmanyidenticalparticles 4.Numberrepresentationofsystemsofidenticalparticles 5.Anassemblyofbosons 6.AnassemblyoffermionsAPPENDIXA.FINITE-DIMENSIONALVECTORSPACES 1.Basicdefinitions 2.Operatorsinunitaryspaces 3.Thespectraltheorem 4.Thetensorproduct 5.Antilinearoperators 6.Wigner'stheoremAPPENDIXB.THEHILBERTSPACE 1.Basicdefinitions,unboundedoperators 2.Thespectraltheorem 3.FunctionspacerepresentationAPPENDIXC.DIRAC'SFORMULATIONINTHEHILBERTSPACE 1.Tempereddistributions 2.GeneralizationtoanarbitraryHilbertspace 3.Dirac'sformulationAPPENDIXD.AREMINDERFROMCLASSICALMECHANICS 1.Canonicaltransformations 2.AreminderfromclassicalmechanicsNOTESBIBLIOGRAPHYINDEX
