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首页 Quantum Mechanics 狄拉克英文教材.pdf

Quantum Mechanics 狄拉克英文教材.pdf

Quantum Mechanics 狄拉克英文教材.pdf

上传者: 逍遥飘仙 2013-09-15 评分 0 0 0 0 0 0 暂无简介 简介 举报

简介:本文档为《Quantum Mechanics 狄拉克英文教材pdf》,可适用于高等教育领域,主题内容包含SCIENCETHEINTERNATIONALSERIESOFMONOGRAPHSONPHYSICSGENERALEDITORSWMARSHALL,符等。

SCIENCETHEINTERNATIONALSERIESOFMONOGRAPHSONPHYSICSGENERALEDITORSWMARSHALL,DHWILKINSONTHEINTERNATIONALSERIESOFMONOGRAPHSONPHYSICSAlreadyPublishedTHETHEORYOFELECTRICANDMAGNETICSUSCEPTIBILITIESByJ,HVANVLECKTHETHEORYOFATOMICCQLLISIONSByNFMOTTandHswMASSEYThirdeditionRELATIVITY,THERMODYNAMICS,A~~COSMOLOGYByRCTOLMANKINEMATICRELATIVITYAsequeltoRelativity,Gravitation,andWorldStructureByEA:MU,NETHEPRINCIPLESOFSTATISTICAL~IECHANICSByRCTOLMANELECTRONICPROCESSESINIONICCRYSTALSByNFMOTTandRwGURNEYSecondeditionGEOMAGNETISMBySCHAPMANandJBARl'ELSvolsTHESEPARATIONOFGASESByMR"OREMANNSecondeditionTHEPRINCIPLES'OFQUANTUMMECHANICSBy:pAMDIMeFourtheditionTHEORYOFATOMICNUCLEUSANDNUCLEARENERGYSOURCESByGGAMOWandcLCltlTClJFIELDBeingthethirdeditionofSTRUCTUREOFATOMICNUCLEUSANDNUCLEARTRANSFORMATIONSTHEPULSATIONTHEORYOFVARIABLESTARSBysROSSELANDTHEORYOFPROBABILITYByHAROLDJEFFREYSThirdeditionTHEFRICTIONANDLUBRICATIONOFSOLIDSByFPllOWD:ENandDTABORPartPartIIELECTRONICANDIONICIMPACTPHENOMENAByHsWMASSEYandEHSlJURBOPMIXTURESByEAGUGGENHEIMTHETHEORYOFRELATIVITYByCrLLERTHEOUTERLAYERSOFASTARByRvdRWOQLLEyandDwNSTIBBSDISLOCATIONSANDPLASTICFLOWINCRYSTALSByARCOTTRELLELECTRICALBREAKDOWNOFGASESByJMMEEKandJDCltAQQSGEOCHEMISTRYBythelatevMGOLDSCHMIDTEditedbyALEXMUIRTHEQUANTUMTHEORYOFRADIATIONBywHEITLERThirdeditionONTHEORIGINOFTHESOLARSYSTEMByHALFVÉNDYNAMICALTHEORYOFCRYSTALLATTICESByMBORNandxHUANQMETEORASTRONOMYByACBLOVELLRECENTADVANCESINOPTICSByEHLINFOOTQUANTUMTHEORYOFSOLIDSByREPEIERLSMOLECULARBEAMSByNORMANFRAMSEYNEUTRONTRANSPORTTHEORYByBDAVISONwiththecollaborationofJBSPKESRECTIFYINGSEMICONDUCTORCONTACTSByHKHENISCHTHETHEORYOFELEMENTARYPARTICLESByJHAMILTONELECTRONSANDPHONONSByJM~ZIMANHYDRODYNAMICANDHYDROMAGNETICSTABILITYBysCHANDRASERHARTHEPRINCIPLESOFNUCLEARMAGNETISMByAABRAGAMCOSlIICALELECTRODYNAMICS:FundamentalPrincipIesByHALFVÉNandCClFALTHAMMARSecondeditionTHEORYANDPRACTICEOFTHEEVALUATIONOFMEASUREMENTSByLJÁNOSSYTHEPRINCIPLESQUANTUMMJi~CIIANICSBYPAThIDIRA(jLUCASIA~PROFESSOROF~ATHEM!TICSIl'lTnEUNIVERSITYOFCAMDRIlWFOURTHEDITION(Revised)OXFORDATTHECLARENDONPRESS•OxfordUniversityPress,ElyHouse,LondonWGLASGOWNEWYORKTORONTOMELBOURNEWELLINGTONCAPETOWNSALISBURYIBADANNAIROBILUSAKAADDISABABABOMBAYCALCUTTAMAD,RASKARACHILAHOREDACCAKUALALUMPURHONGKONGTOKYO~OxfordUniversityPressISr=r=~~~AFIRSTEDITIONSECONDEDITIONTHIRDEDITIONREPRINTEDLITHOGRAPHICALLYINGREATBRITAINAT'rllEUNIVERSITYPRESS,OXBORDFROMSHEETSOFTHETHIRDEDITION,,IFOURTHEDITIONREPRIN'l'El),,,PREFACETOTHEFOURTHEDITIONTHEmainchangefromthethirdeditionisthatthechapteronquantumelectrodynamicshasbeenrewrittenThequantulnelectrodynamicsgiveninthethirdeditiondescribesthemotionofindividualchargedparticlesmovingthroughtheelectromagneticfield,incloseanalogywithclassicalelectrodynamicsItisaformoftheoryinwhichthenumberofchargedparticlesisconservedanditcannotbegeneralizedtoallowofvariationofthenumberofchargedparticlesInpresentdayhighenergyphysicsthecreationandannihilationofchargedparticlesisafrequentoccurrenceAquantumelectrodynamicswhichdemandsconservationofthenumberofchargedparticlesisthereforeoutoftouchwithphysicalrealitySohavereplaceditbyaquantumelectrodynamicswhichincludescreationandannihilationofelectronpositronpairsThisinvolvesabandoninganycloseanalogywithclassicalelectrontheory,butprovidesacloserdescriptionofnatureItseemsthattheclassicalconceptofanelectronisnolongerausefulmodelinphysics,exceptpossiblyforelementarytheoriesthatarerestrictedtolowenergyphenomenaSTJOHN'SCOLLEGE,CAMBRIDGEMayPÁMDNOTETOTHEREVISIONOFTHEFOURTHEDITIONTHEopportunityhasbeentakenofrevisingpartsofChapterXII('Quantumelectrodynamics')andofaddingtwonewsectionsoninterpretationandapplicationsPÁMDSToJOHN'ISCOII,FGE,CAMBRIDGEMayFROlVITHEPREFACETOTHEFIRSTEDITIONTHEmethodsofprogressintheoreticalphysicshaveundergoneavastchangeduringthepresentcenturyTheclassicaltraditionhasbeentoconsidertheworldtobeanassociationofobservableobjects(particles,fluids,fields,etc)movingaboutaccordingtodefinitelawsofforce,sothatonecouldformamentalpictureinspaceandtimeofthewholeschemeThisledtoaphysicswhoseaiIDwastomakeassumptionsaboutthemechanismandforcesconnectingtheseobservableobjects,toaccountfortheirbehaviourinthesimplestpossiblewayIthasbecomeincreasinglyevidentinrecenttimes,however,thatnatureworksonadifferentplanHerfundamentallawsdonotgovemtheworldasitappearsinourmentalpictureinanyverydirectway,butinsteadtheycontrolasubstratumofwhichwecannotformamentalpicturewithoutintrof:ducingirrelevanciesTheformulationoftheselawsrequirestheuseofthemathematicsoftransformationsTheimportantthingsintheworldappearastheinvariants(ormoregenerallythenearlyinvariants,orquantitieswithsimpletransformationproperties)ofthesetransformationsThethingsweareimmediatelyawareofaretherelationsofthesenearlyinvariantstoacertainframeofreference,usuallyonechosensoastointroducespecialsimplifyingfeatureswhichareunimportantfromthepointofviewofgeneraltheoryTliegrowthoftheuseoftransformationtheory,asappliedfirsttorelativityandlatertothequantumtheory,istheessenceofthenewmethodintheoreticalphysicsFurtherprogressliesinthedirectionofmakingourequationsinvariantunderwiderandstill,vidertransformationsThisstateofaffairsisverysatisfactoryfromaphilosophicalpointofview,asimplyinganincreasingrecognitionofthepartplayedbytheobserverinhimselfintroducingtheregularitiesthatappearinhisobservations,andalackofarbitrarinessinthewaysofnature,butitmakesthingslesseasyfortheleamerofphysicsThenewtheories,ifonelooksapartfromtheirmathematicalsetting,arebuiltupfromphysicalconceptswhichcannotbeexplainedintermsofthingspreviouslyknowntothestudent,whichcannotevenbeexplainedadequatelyinwordsatallLikethefundamentalconcepts(egproximity,identity)whicheveryonemustlearnonhisVIIIPREFACETOFIRSTEDITIONarrivalintotheworld,thenewerconceptsofphysicscanbemasteredonlybylongfamiliaritywiththeirpropertiesalldusesFromthemathematicalsidetheapproachfothenewtheoriespresentsnodifficulties,asthemathematicsrequired(atanyratethatwhichisrequiredforthedevelopmentofphysicsuptothepresent)isnotessentiallydifferentfromwhathasbeencurrentforaconsiderabletimelatllematicsisthetoolspeciallysuitedfordealingwithabstractconceptsofanykindandthereisnolimittoitspowerinthisfieldForthisreasonabookonthenewphysics,ifnotpurelydescriptiveofexperimentalwork,mustbeessentiallymathematicalAHthesamethemathematicsisonlyatoolandoneshouldlearntoholdthephysicalideasinone'smindwithoutreferencetothemathematicalformoInthisbookhavetriedtokeeptJlephysicstotheforefront,bybeginningwithanentirelyphysicalchapteraridinthelaterworkexaminingthephysicalmeaningundel'IyingtheformalismwhereverpossibleTheamountoftheoreticalgroundonehastocoverbeforebeingabletosolveproblemsofrealpracticalvalueisratherlarge,butthiscircumstanceisaninevitableconsequenceofthefundamentalpartplayedbytransforlnationtheoryandislikelytobecomenlorepronouncedinthetheoreticalphysicsofthefutureWithregardtothemathematicalforulinwhichthetheorycanbepresented,anauthormustdecideattlieoutsetbetweentwomethodsThereisthesymbolicmethod,whichdealsdirectlyinanabstractwaywiththequantitiesoffundamentalimportance(theinvariants,etc,ofthetransformations)andthereisthenlethodofcoordinatesorrepresentations,whichdealswithsetsofnumberscorrespondingtothesequantitiesThesecondofthesehasusuallybeenusedforthepresentationofquantummechanics(infactithasbeenusedpracticallyexclusivelywiththeexceptionofWeyl'sbookGruppentheorieundQuantenmechanik)Itisknownunderoneorotherofthetwonames'WaveMechanics'and'MatrixMechanics'accordingtowhichphysicalthingsreceiveemphasisinthetreatment,thestatesofasystemoritsdynamicalvariablesIthastheadvantagethatthekindofmathematicsrequiredismorefamiliartotheaveragestudent,andalsoitisthehistoricalmethodThesymbolicmethod,however,seemstogomoredeeplyintothenatureofthingstenablesonetoexuressthephysicalla",~sinaneatandconciseway,andwiHprobablyLeincreasinglyusedinthefutureasitbecomesbetterunderstoodanditsownspecialmathematicsgetsPREFACETOFIRSTEDITIONIXdevelopedForthisreasonhavechosenthesymbolicmethod,introducingtherepresentativeslatermerelyasanaidtopracticalcalculationThishasnecessitatedacompletebreakfromthehistoricallineofdevelopment,butthisbreakisanadvantagethroughenablingtheapproachtothenewideastobemadeasdirectaspossibleSToJOHN'SCOLLEGE,CAMBRIDGEMayPÁMDCONTENTSlTHEPRINCIPLEOFSUPERPOSITIONTheNeedforaQuantumTheoryThePolarizationofPhotonsInterferenceofPhotonsSuperpositionandIndeterminacyMathematicalFormulationofthePrincipIeBraandKetVectors•IrDYNAMICALVARIABLESANDOBSERVABLES•LinearOperatorsConjugateRelations•EigenvaluesandEigenvectorsObservablesFunctionsofObservablesTheGeneralPhysicalInterpretationCommutabilityandCompatibilityREPRESENTATIONSBasicVectorsTheOFunctionPropertiesoftheBasicVectorsTheRepresentationofLinearOperatorsProbabilityAmplitudesTheoremsaboutFunctionsofObservablesDevelopmentsinNotationIVTHEQUANTUMCONDITIONSPoissonBracketsSchrdinger'sRepresentationTheMomentumRepresentationHeisenberg'sPrincipIeofUncertaintyDisplacementOperatorsUnitaryTransformationsVTHEEQUATIONSOFMOTIONSchrodinger'sFormfortheEquationsofMotionHeisenberg'sFormfortheEquationsofMotionStationaryStatesTheFreeParticleTheMotionofWavePackets•TheActionPrincipIeTheGibbsEnsemble•VIELEMENTARYAPPLICATIONSTheHarmonicOscillatorAngularMomentumCONTENTSaüPropertiesofAngularMomentumTheSpinoftheElectronMotioninaCentralFieldofForceEnergyIevelsoftheHydrogenAtomSelectionRulesTheZeemanEffectfortheHydrogenAtomVILPERTURBATIONTHEORYGeneralRemarksTheChangeintheEnergyIevelscausedbyaPerturbationThePerturbationconsideredascausingTransitionsApplicationtoRadiationTransitionscausedbyaPerturbationIndependentoftheTimeTheAnomalousZeemarE:flectVITCOLLISIONPROBLFMSGeneralRemarksTheScatteringCoefficientSolutionwjththeMomentumRepresentationDispersiveScatteringResonanceScatteringEmissionandAbsorptionIXSYSTEMSCONTAINil'fGSEVERALSIMILARPARTICLESSymmetricalandAntisymmetricalStatesPermutationsasDynarnicdVariablesPermutationsasConstantsoftheMotionDeterminationoftheEnergyIevelsApplicationtoElectronsXTHEORYOFRADIATIONAnAssemblyofBosonsTheCormexionbetweenBosonsandOscillatorsEmissionandAbsorptionofBosonsApplicationtoPhotonsTheInteractionEnergybetweenPhotonsandanAtomEmission,Absorption,andScatteringofRadiationAnAssemblyofFermionsXIRELATIVISTICTHEORYOFTHEELECTRONRelativisticTreatmentofaParticleTheWaveEquationfortheElectronInvarianceunderaLorentzTransformationTheMotionofaFreeElectronExistenceoftheSpinTransitiontoPolarVariablesTheFinestructureoftheEnergyIevelsofHydrogenTheoryofthePositron••XIICONTENTSXIIQUANTUMELECTRODYNAMICSTheElectromagneticFieldintheAbsenceofMaterRelativisticFormoftheQuantumConditionsTheDynamicalVariablesatoneTimeTheSupplementaryConditionsElectronsandPositronsbyThemselves~TheInteractionThePhvsicalVariablesInterpretationApplicationsINDEX•THEPRINCIPLEOFSUPERPOSITIONTheneedforaquantumtheoryCLASSIOALmechanicshasbeendevelopedcontinuouslyfromthetimeofNewtonandappliedtoaneverwideningrangeofdynamicalsystems,includingtheelectromagneticfieldininteractionwithmatterTheunderlyingideasandthelawsgoverningtheirapplicationformasimpleandelegantscheme,whichonewouldbeinclinedtothinkcouldnotbeseriouslymodifiedwithouthavingallitsattractivefeaturesspoiltNeverthelessithasbeenfoundpossibletosetupanewscheme,calledquantummechanics,whichismoresuitableforthedescriptionofphenomenaontheatomicscaleandwhichisinsornerespectsmoreelegantandsatisfyingthantheclassicalschemeThispossibilityisduetothechangeswhichthenewschemeinvolvesbeingofaveryprofoundcharacterandnotclashingwiththefeaturesoftheclassicaltheorythatmakeitsoattractive,asaresultofwhichallthesefeaturescanbeincorporatedinthenewschemeThenecessityforadeparturefromclassicalmechanicsisclearlyshownbyexperimentalresultsInthefirstplacetheforcesknowninclassicalelectrodynamicsareinadequatefortheexplanationoftheremarkablestabilityofatomsandmolecules,whichisnecessaryinorderthatmaterialsmayhaveanydefinitephysicalandchemicalpropertiesatallTheintroductionofnewhypotheticalforceswillnotsavethesituation,sincethereexistgeneralprincipIesofclassicalmechanics,holdingforallkindsofforces,leadingtoresultsindirectdisagreementwithobservationForexample,ifanatomicsystemhasitsequilibriumdisturbedinanywayandisthenleftalone,itwillbesetinoscillationandtheoscillationswillgetimpressedonthesurroundingelectromagneticfield,sothattheirfrequenciesmaybeobservedwithaspectroscopeNowwhateverthelawsofforcegovemingtheequilibrium,onewouldexpecttobeabletoincludethevariousfrequenciesinaschemecomprisingcertainfundamentalfrequenciesandtheirharmonicsThisisnotobservedtobethecaseInstead,thereisobservedanewandunexpectedconnexionbetweenthefrequencies,calledRitz'sCombinationLawofSpectroscopy,accordingto'vhichallthefrequenciescanbeexpressedasdifferencesbetweencertainterms,THEPRINCIPLEOFSUPERPOSITIONthenumberoftermsbeingmuchlessthanthenumberoffrequenciesThislawisquiteunintelligiblefromtheclassicalstandpointOnemighttrytogetoverthedifficultywithoutdepartingfromclassicalmechanicsbyassumingeachofthespectroscopicallyobservedfrequenciestobeafundamentalfrequencywithitsowndegreeoffreedom,thelawsofforcebeingsuchthattheharnlonicvibrationsdonotoccurSuchatheorywillnotdo,however,evenapartfromthefactthatitwouldgivenoexplanationoftheCombinationLaw,sinceitwouldimmediatelybringoneintoconflictwiththeexperimentalevidenceonspecificheatsClassicalstatisticalmechanicsenablesonetoestablishageneralconnexionbetweenthetotalnumberofdegreesoffreedomofanassemblyofvibratingsystemsanditsspecificheatIfoneassumesallthespectroscopicfrequenciesofanatomtocorrespondtodifferentdegreesoffreedom,onewouldgetaspecificheatforanykindofmatterverymuchgreaterthantheobservedvalueInfacttheobservedspecificheatsatordinarytemperaturesaregivenfairlywellbyatheorythattakesintoaccountmerelythemotionofeachatomasawholeandassignsnointernalmotiontoitatallThisleadsustoanewclashbetweenclassicalmechanicsandtheresultsofexperimentoTheremustcertainlybeSOlneinternalmotioninanatomtoaccountforitsspectrum,buttheinternaldegreesoffreedom,forsorneclassicallyinexplicablereason,donotcontributetothespecificheatAsimilarclashisfoundinconnexionwiththeenergyofoscillationoftheelectromagneticfieldinavacuumClassicalmechanicsrequiresthespecificheatcorrespondillgtothisenergytobeinfinite,butitisobservedtobequitefiniteAgeneralconclusionfromexperimentalresultsisthatoscillationsofhighfrequencydonotcontributetheirclassicalquotatothespecificheatAsanotherillustrationofthefailureofclassicalmechalicswemayconsiderthebehaviourofLightWehave,ontheonehand,thephenomenaofinterferenceanddiffraction,whichcanbeexplainedonyonthebasisofawavetheoryontheother,phenomenasuchasphotoelectricemissionandscatteringbyfreeelectrons,whichshowthatlightiscomposedofsllallparticlesTheseparticles,whicharecalledphotons,haveeachadefiniteenergyandmomentum,dependingonthefrequencyofthelight,andappeartohavejustasrealanexistenceaselectrons,oranyotherparticlesknovninphysicsAfractionofaphotonisneverobservedTHENEEDFORAQUANTUMTHEORYExperimentshaveshownthatthisanomalousbehaviourisnotpeculiartolight,butisquitegeneralAHmaterialparticleshavewaveproperties,whichcanbeexhibitedundersuitableconditionsWehavehereaverystrikingandgeneralexalnpleofthebreakdownofclassicalmechanicsnotmerelyaninaccuracyinitslawsofmotion,butaninadequacyofitsconceptstosupplyuswithadescriptionofatomiceventsThenecessitytodepartfromclassicalideaswhenonewishestoaccountfortheultimatestructureofmattermaybeseen,notonlyfromexperimentallyestablishedf

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