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1、F.J.DysonADVANCEDQUANTUMMECHANICSSecondEditionarXiv:quant-ph/0608140v118Aug2006ADVANCEDQUANTUMMECHANICSLecturenotesbyProfessorF.J.DysonforacourseinRelativisticQuantumMechanicsgivenatCornellUniversityintheFallof1951.SecondEditionThe?rsteditionofthesenoteswaswrittenbyProfessorDyson.Thesecondeditionwas
2、preparedbyMichaelJ.Moravcsik;heisresponsibleforthechangesmadeintheprocessofre-editing.Generallyusednotation:A?:complexconjugatetransposed(Hermitianconjugate)A+:complexconjugate(nottransposed)A:A?β=A?γ=adjoint4A?1=inverseAT=transposedI=identitymatrixoroperatoriTableofContentsIntroduction1SubjectMatte
3、r..............................................1DetailedProgram.............................................2OneParticleTheories..........................................2TheDiracTheory4TheFormoftheDiracEquation....................................4LorentzInvarianceoftheDiracEquation.................
4、..............6ToFindtheS...............................................7TheCovariantNotation.........................................8ConservationLaws–ExistenceofSpin.................................9ElementarySolutions...........................................10TheHoleTheory......................
5、.......................11PositronStates–chargeconjugation..................................11ElectromagneticPropertiesoftheElectron..............................12TheHydrogenAtom...........................................13Solutionoftheradialequation.....................................14Behaviorofa
6、nElectroninnon-relativisticapproximation......................17SummaryofMatricesintheDiracTheoryinournotation......................20SummaryofMatricesintheDiracTheoryintheFeynmannotation................21ScatteringProblemsandBornApproximation22GeneralDiscussion......................................
7、......22ProjectionOperators...........................................23CalculationofSpurs...........................................24ScatteringoftwoelectronsinBornApproximation–TheM?llerFormula.....
