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经典和量子动力学 第2版

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经典和量子动力学 第2版

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定 价：￥56.00

作 者：W.Dittrich/等 著

出 版 社：世界图书出版公司

出版时间：1998-3-1

I S B N：7506236249

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    内容简介

    片断：
    Thatquantumandclassicalmechanicsare,infact,disjointphysicalworldswas
    clearfromthcvcrybeginning.Present-dayexperienceisnoexception;itisrathcr
    embarrassingtofindoutthatanimportantgeometricphaseinacyclicadiabatic
    quantalprocesshasbecnoverlookedsincethedawnofquantummechanics.This
    so-calledBcrryphasesignalsthatinnonrelarivisricaswellasrelativisticquantum
    thcory,geomctricalmetbodsplayaneminentrole.
    Theappearanceoftopologyinquantummcchanicsisprobablythemostim-
    ponantnewdevelopmemtooccurinrecentyears.Alargeportionofthistextis
    thereforedevotedtothegeometricstructureoftopologicallynontrivialphysical
    systcms.Berryphases,Maslovindices,Chem-Simonstennsandvariousother
    topologicalquantitieshaveclearlydcmonstratcdthatquantummcchanicsisnot,
    asofyct,acloscdbook.
    1.TheActionPrinciplesinMechanics
    Webcginthischaptcrwiththedcfinitionoftheactionfuncdonalastimeintcgral
    overtheLagrangianL(q(t),q(t);t)ofadynamicalsystcm:
    Here,qi,i=1,2,...,N,arepointsinN-dimcnsionalconfigurationspace.Thus
    qi,(t)describcsthemodonofthesystem,andqi(t)=dq/dtdctennincsitsvelocity
    alongthcpathinconfiguradonspacc.Thccndpointsofthctrajectoryaregivcnby
    qi(t1)=qil.andq1(t2)=qi2.
    Nextwewanttofindoutwhattheactualdynamicalpathofthesystemis.The
    answeriscontainedintheprincipleofstadonaryaction:inresponsctoinfinitcsimal
    variadonoftheintegrationpath,theactionSisstationary,SS=0,forvariations
    aboutthecorrectpath,providedtheinitialandfinalconfigurationsarcheldflxed.
    Ontheotherhand,ifwepermitinfinitesimalchangesofqi(t)attheinitialand
    finaldmes,includingalteradonsofthosedmes,theonlycontribudontoSScomes
    fromtheendpointvariadons,or
    SS=G(t2)-G(t1).(1.2)
    Eq,adon(1.2)isthemostgcneralformuladonoftheacdonprincipleinmechanics.
    ThexcdvaluesGiandG2dependonlyonthecndpointpathvariablesatthe
    respeaiveterminaldmes.
    Agin,givenasystemwiththeacdonfuncdonalS,theactualdmecvoludon
    inconfignrationspacefollowsthatpathaboutwhichgencralvariadonsproduce
    onlyendpintcontribudons.TheexplicitfonnofGisdependentuponthespccial
    rcprescntationoftheacdonprinciple.Inthcfollowingwebeginwiththeonethat
    isbestknow.i.e.

    作者简介

    目录

    Contents
    Introduction
    1.TheActionPrinciplesinMechanics
    2.ApplicationoftheActionPrinciples
    3.JacobiFields,ConjugatcPoints
    4.CanonicalTransfonnations
    5.TheHamilton-JacobiEquation
    6.Action-AngleVariables
    7.TheAdiabaticInvarianceoftheActionVariables
    8.Time-IndcpendcntCanonicalPcrturbarionThcory
    9.CanonicalPenurbationTheorywithScvcralDcgreesofFrcedom
    10.CanonicalAdiabaticTheory
    11.RemovalofResonances
    12.SupcrconvergentPenurbationThcory,KAMThcorem(Introduction)
    13.PoincareSuifaccofScctions,Mappings
    14.TheKAMTncorem
    15.FundamentalPrinciplesofQuantumMechanics
    16.ExamplesforCalcularingPathIntcgrals
    17.DirectEvalutionofPathIntcgrals
    18.LincarOscillorwithTime-DcpendcntFrequency
    19.PropagatorsforParticlesinanExtemalMagncticFicld
    20.SimpleApplktionsofPropagatorFunctions
    21.TheWKBAproximation
    22.PartitionFunconfortheHamonicOscillator
    23.IntroducriontoHomotopyTheory
    24.ClassicalChem-SimonsMechanics
    25.SemiclassicalQuantization
    26.Thc"MaslovAnomaly"forthcHannonicOscillator
    27.MaslovAnomalyandtheMorseIndexTheorem
    28.Beny'sPhasc
    29.ClassicalAnaloguestoBcrry'sPhase
    30.BenyPhaseandParametricHannonicOscillator
    31.TopologicalPhasesinPlanarElcctrodynamics
    References
    SubjectIndcx

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