苏汝铿高等量子力学讲义(英文版)Chapter3Relat汇总课件

Chapter3

RelativisticQuantumMechanicsChapter3

RelativisticQuantum1苏汝铿高等量子力学讲义(英文版)Chapter3-Relat汇总课件2IntroductionNon-relativisticquantummechanicsrelativisticquantummechanicsSchrödingerequationKlein-GordonequationS~integerDiracequationS~halfintegerSpinisautomaticallycontainedinDiracequationIntroductionNon-relativisticq3§3.1Klein–GordonequationLorentztransormationtime,spaceareofthesameweightK–Gequation§3.1Klein–GordonequationLo4§3.1Klein–Gordonequation§3.1Klein–Gordonequation5§3.1Klein–Gordonequation§3.1Klein–Gordonequation6§3.1Klein–Gordonequation§3.1Klein–Gordonequation7§3.1Klein–GordonequationDiscussionNegativeenergyinstable§3.1Klein–GordonequationDi8§3.1Klein–GordonequationNegativeprobability§3.1Klein–GordonequationNe9§3.1Klein–Gordonequation§3.1Klein–Gordonequation10§3.1Klein–GordonequationNon-relativisticlimit:K-GeqScheq§3.1Klein–GordonequationNo11§3.1Klein–Gordonequation§3.1Klein–Gordonequation12§3.1Klein–Gordonequation§3.1Klein–Gordonequation13§3.1Klein–GordonequationWithelectromagneticfield§3.1Klein–GordonequationWi14§3.1Klein–Gordonequation§3.1Klein–Gordonequation15§3.1Klein–GordonequationCovariantform§3.1Klein–GordonequationCo16§3.1Klein–Gordonequation§3.1Klein–Gordonequation17§3.1Klein–Gordonequation§3.1Klein–Gordonequation18§3.1Klein–Gordonequation§3.1Klein–Gordonequation19§3.2DiracequationHowtoovercomethenegativeprobabilitydifficulty§3.2DiracequationHowtoover20§3.2Diracequation§3.2Diracequation21§3.2Diracequation§3.2Diracequation22§3.2Diracequation§3.2Diracequation23§3.2DiracequationTheconditionforαandβ

1)Theymustfollowtherelation 2)OperatorHmustbeHermitian 3)Lorentzinvariance§3.2DiracequationTheconditi24§3.2Diracequation§3.2Diracequation25§3.2Diracequation§3.2Diracequation26§3.2Diracequation§3.2Diracequation27§3.2Diracequation4anti-commutematricesαandβ4×4matrices§3.2Diracequation4anti-comm28§3.2Diracequation§3.2Diracequation29§3.2DiracequationConservationlawoftheprobabilityflux§3.2DiracequationConservatio30§3.2Diracequation§3.2Diracequation31§3.2Diracequation§3.2Diracequation32§3.3solutionsofthefreeparticle§3.3solutionsofthefreepar33§3.3solutionsofthefreeparticle§3.3solutionsofthefreepar34§3.3solutionsofthefreeparticle§3.3solutionsofthefreepar35§3.3solutionsofthefreeparticle§3.3solutionsofthefreepar36§3.3solutionsofthefreeparticle§3.3solutionsofthefreepar37§3.3solutionsofthefreeparticle§3.3solutionsofthefreepar38§3.3solutionsofthefreeparticle§3.3solutionsofthefreepar39§3.3solutionsofthefreeparticle§3.3solutionsofthefreepar40§3.3solutionsofthefreeparticleDiscussionPositiveenergystate(λ=+1)Negativeenergystate(λ=-1)Eigenstatesofmomentump§3.3solutionsofthefreepar41§3.3solutionsofthefreeparticleOrbitalangularmomentumisnotconserved§3.3solutionsofthefreepar42§3.3solutionsofthefreeparticle§3.3solutionsofthefreepar43§3.3solutionsofthefreeparticleSpinangularmomentumOr§3.3solutionsofthefreepar44§3.3solutionsofthefreeparticle§3.3solutionsofthefreepar45§3.3solutionsofthefreeparticle§3.3solutionsofthefreepar46§3.3solutionsofthefreeparticle§3.3solutionsofthefreepar47§3.3solutionsofthefreeparticleHelicityoperator§3.3solutionsofthefreepar48§3.3solutionsofthefreeparticle§3.3solutionsofthefreepar49§3.3solutionsofthefreeparticleIf,wefindEigenvalues:§3.3solutionsofthefreepar50§3.3solutionsofthefreeparticleEigenstates:§3.3solutionsofthefreepar51§3.3solutionsofthefreeparticle§3.3solutionsofthefreepar52§3.3solutionsofthefreeparticleDiracholetheoryDiracseaHole:(+Ep>0,+m>0,+e>0)(positron)1932,Andersondiscoveredpositronfromcosmicrayusingcloudchamber§3.3solutionsofthefreepar53§3.4DiracequationinthecentralforcefieldEquationinnon-relativisticlimit§3.4Diracequationinthecen54§3.4Diracequationinthecentralforcefield§3.4Diracequationinthecen55§3.4Diracequationinthecentralforcefield§3.4Diracequationinthecen56§3.4DiracequationinthecentralforcefieldInnon-relativisticapproximation§3.4Diracequationinthecen57§3.4Diracequationinthecentralforcefield§3.4Diracequationinthecen58§3.4Diracequationinthecentralforcefield§3.4Diracequationinthecen59§3.4Diracequationinthecentralforcefield§3.4Diracequationinthecen60§3.4DiracequationinthecentralforcefieldNoting:uptotheorderNormalizationconditionmustbeensured§3.4Diracequationinthecen61§3.4Diracequationinthecentralforcefield§3.4Diracequationinthecen62§3.4Diracequationinthecentralforcefield§3.4Diracequationinthecen63§3.4Diracequationinthecentralforcefield§3.4Diracequationinthecen64§3.4Diracequationinthecentralforcefield§3.4Diracequationinthecen65§3.4DiracequationinthecentralforcefieldByusing§3.4Diracequationinthecen66§3.4DiracequationinthecentralforcefieldRelativisticcorrectionofkineticenergy§3.4Diracequationinthecen67§3.4DiracequationinthecentralforcefieldThomastermDarwinterm§3.4Diracequationinthecen68§3.4Diracequationinthecentralforcefield§3.4Diracequationinthecen69§3.4DiracequationinthecentralforcefieldQuantumnumberK§3.4Diracequationinthecen70§3.4Diracequationinthecentralforcefield§3.4Diracequationinthecen71§3.4Diracequationinthecentralforcefield§3.4Diracequationinthecen72§3.4Diracequationinthecentralforcefield§3.4Diracequationinthecen73§3.4Diracequationinthecentralforcefield§3.4Diracequationinthecen74§3.4Diracequationinthecentralforcefield§3.4Diracequationinthecen75§3.4Diracequationinthecentralforcefield§3.4Diracequationinthecen76§3.4Diracequationinthecentralforcefield§3.4Diracequationinthecen77§3.4Diracequationinthecentralforcefield§3.4Diracequationinthecen78§3.4DiracequationinthecentralforcefieldRadialequations§3.4Diracequationinthecen79§3.4Diracequationinthecentralforcefield§3.4Diracequationinthecen80§3.4Diracequationinthecentralforcefield§3.4Diracequationinthecen81§3.4Diracequationinthecentralforcefield§3.4Diracequationinthecen82§3.4DiracequationinthecentralforcefieldWetake§3.4Diracequationinthecen83§3.5SolutionoftheDiracequationintheCoulombfieldMotivationDiscussiontheHydrogenatomFinestructure§3.5SolutionoftheDiracequ84§3.5SolutionoftheDiracequationintheCoulombfield§3.5SolutionoftheDiracequ85§3.5SolutionoftheDiracequationintheCoulombfield§3.5SolutionoftheDiracequ86§3.5SolutionoftheDiracequationintheCoulombfield§3.5SolutionoftheDiracequ87§3.5SolutionoftheDiracequationintheCoulombfield§3.5SolutionoftheDiracequ88§3.5SolutionoftheDiracequationintheCoulombfield§3.5SolutionoftheDiracequ89§3.5SolutionoftheDiracequationintheCoulombfieldn’=0,1,2,…,n=1,2,3…§3.5SolutionoftheDiracequ90§3.5SolutionoftheDiracequationintheCoulombfield§3.5SolutionoftheDiracequ91§3.5SolutionoftheDiracequationintheCoulombfieldGroundstate1S1/2(n=0,κ=-1,n=1,j=1/2)§3.5SolutionoftheDiracequ92§3.5SolutionoftheDiracequationintheCoulombfield§3.5SolutionoftheDiracequ93§3.5SolutionoftheDiracequationintheCoulombfield§3.5SolutionoftheDiracequ94§3.5SolutionoftheDiracequationintheCoulombfieldQuestionDiraceq+non-relativisticlimitScheqZ≥137?NolimitforZUniformchargedsphere?NolimitforZFinestructureEnjEnforScheq§3.5SolutionoftheDiracequ95§3.6KleinparadoxAnotherquestionforthenon-relativisticlimitofDiracequationDoespositronexistScalarlikepotentialandvectorlikepotential§3.6KleinparadoxAnotherques96§3.6Kleinparadox§3.6Kleinparadox97§3.6Kleinparadox§3.6Kleinparadox98§3.6KleinparadoxAttheinfinity,thewavefunctionisnotzero,whichmeansthatthereisonlythescatteringstatesolutioninsteadofboundstatesolution§3.6KleinparadoxAttheinfin99§3.6KleinparadoxDiracequation(non-relativisticlimit)ScheqV(r)=grV(r)=grψ|r∞oscillatingΨ|r∞0ScatteringstatesBoundstatesCannotconfinequarksconfinement§3.6KleinparadoxDiracequati100§3.6KleinparadoxThephysicsofKleinparadox§3.6KleinparadoxThephysics101§3.6Kleinparadox§3.6Kleinparadox102§3.6Kleinparadox§3.6Kleinparadox103§3.6Kleinparadox§3.6Kleinparadox104§3.6Kleinparadox§3.6Kleinparadox105§3.6Kleinparadox§3.6Kleinparadox106§3.6Kleinparadox§3.6Kleinparadox107§3.6Kleinparadox§3.6Kleinparadox108§3.6Kleinparadox§3.6Kleinparadox109§3.6Kleinparadox§3.6Kleinparadox110§3.6Kleinparadox§3.6Kleinparadox111§3.6Kleinparadox§3.6Kleinparadox112§3.6Kleinparadox§3.6Kleinparadox113§3.6Kleinparadox§3.6Kleinparadox114§3.6KleinparadoxIfp=mc§3.6KleinparadoxIfp=mc115§3.6KleinparadoxTheexplanationofKleinparadox§3.6KleinparadoxTheexplanat116§3.6Kleinparadox§3.6Kleinparadox117§3.6Kleinparadox§3.6Kleinparadox118§3.6Kleinparadox§3.6Kleinparadox119§3.6Kleinparadox§3.6Kleinparadox120§3.6Kleinparadox§3.6Kleinparadox121§3.6Kleinparadox§3.6Kleinparadox122§3.6Kleinparadox§3.6Kleinparadox123§3.6Kleinparadox§3.6Kleinparadox124§3.7MITbagmodelMotivation:canweestablishamodeltoconfinequarkscalarlikepotential§3.7MITbagmodelMotivation:125§3.7MITbagmodel§3.7MITbagmodel126§3.7MITbagmodel§3.7MITbagmodel127§3.7MITbagmodelIntroducingscalarlikepotential§3.7MITbagmodelIntroducing128§3.7MITbagmodel§3.7MITbagmodel129§3.7MITbagmodel§3.7MITbagmodel130§3.7MITbagmodelWheng’>gwefindaexponentiallydecayingsolution§3.7MITbagmodelWheng’>gwe131§3.7MITbagmodelSolutionofstepfunction§3.7MITbagmodelSolutionof132§3.7MITbagmodel§3.7MITbagmodel133§3.7MITbagmodel§3.7MITbagmodel134§3.7MITbagmodel§3.7MITbagmodel135§3.7MITbagmodel§3.7MITbagmodel136§3.7MITbagmodel§3.7MITbagmodel137§3.7MITbagmodel§3.7MITbagmodel138§3.7MITbagmodel§3.7MITbagmodel139苏汝铿高等量子力学讲义(英文版)Chapter3-Relat汇总课件140Chapter3

RelativisticQuantumMechanicsChapter3

RelativisticQuantum141苏汝铿高等量子力学讲义(英文版)Chapter3-Relat汇总课件142IntroductionNon-relativisticquantummechanicsrelativisticquantummechanicsSchrödingerequationKlein-GordonequationS~integerDiracequationS~halfintegerSpinisautomaticallycontainedinDiracequationIntroductionNon-relativisticq143§3.1Klein–GordonequationLorentztransormationtime,spaceareofthesameweightK–Gequation§3.1Klein–GordonequationLo144§3.1Klein–Gordonequation§3.1Klein–Gordonequation145§3.1Klein–Gordonequation§3.1Klein–Gordonequation146§3.1Klein–Gordonequation§3.1Klein–Gordonequation147§3.1Klein–GordonequationDiscussionNegativeenergyinstable§3.1Klein–GordonequationDi148§3.1Klein–GordonequationNegativeprobability§3.1Klein–GordonequationNe149§3.1Klein–Gordonequation§3.1Klein–Gordonequation150§3.1Klein–GordonequationNon-relativisticlimit:K-GeqScheq§3.1Klein–GordonequationNo151§3.1Klein–Gordonequation§3.1Klein–Gordonequation152§3.1Klein–Gordonequation§3.1Klein–Gordonequation153§3.1Klein–GordonequationWithelectromagneticfield§3.1Klein–GordonequationWi154§3.1Klein–Gordonequation§3.1Klein–Gordonequation155§3.1Klein–GordonequationCovariantform§3.1Klein–GordonequationCo156§3.1Klein–Gordonequation§3.1Klein–Gordonequation157§3.1Klein–Gordonequation§3.1Klein–Gordonequation158§3.1Klein–Gordonequation§3.1Klein–Gordonequation159§3.2DiracequationHowtoovercomethenegativeprobabilitydifficulty§3.2DiracequationHowtoover160§3.2Diracequation§3.2Diracequation161§3.2Diracequation§3.2Diracequation162§3.2Diracequation§3.2Diracequation163§3.2DiracequationTheconditionforαandβ

1)Theymustfollowtherelation 2)OperatorHmustbeHermitian 3)Lorentzinvariance§3.2DiracequationTheconditi164§3.2Diracequation§3.2Diracequation165§3.2Diracequation§3.2Diracequation166§3.2Diracequation§3.2Diracequation167§3.2Diracequation4anti-commutematricesαandβ4×4matrices§3.2Diracequation4anti-comm168§3.2Diracequation§3.2Diracequation169§3.2DiracequationConservationlawoftheprobabilityflux§3.2DiracequationConservatio170§3.2Diracequation§3.2Diracequation171§3.2Diracequation§3.2Diracequation172§3.3solutionsofthefreeparticle§3.3solutionsofthefreepar173§3.3solutionsofthefreeparticle§3.3solutionsofthefreepar174§3.3solutionsofthefreeparticle§3.3solutionsofthefreepar175§3.3solutionsofthefreeparticle§3.3solutionsofthefreepar176§3.3solutionsofthefreeparticle§3.3solutionsofthefreepar177§3.3solutionsofthefreeparticle§3.3solutionsofthefreepar178§3.3solutionsofthefreeparticle§3.3solutionsofthefreepar179§3.3solutionsofthefreeparticle§3.3solutionsofthefreepar180§3.3solutionsofthefreeparticleDiscussionPositiveenergystate(λ=+1)Negativeenergystate(λ=-1)Eigenstatesofmomentump§3.3solutionsofthefreepar181§3.3solutionsofthefreeparticleOrbitalangularmomentumisnotconserved§3.3solutionsofthefreepar182§3.3solutionsofthefreeparticle§3.3solutionsofthefreepar183§3.3solutionsofthefreeparticleSpinangularmomentumOr§3.3solutionsofthefreepar184§3.3solutionsofthefreeparticle§3.3solutionsofthefreepar185§3.3solutionsofthefreeparticle§3.3solutionsofthefreepar186§3.3solutionsofthefreeparticle§3.3solutionsofthefreepar187§3.3solutionsofthefreeparticleHelicityoperator§3.3solutionsofthefreepar188§3.3solutionsofthefreeparticle§3.3solutionsofthefreepar189§3.3solutionsofthefreeparticleIf,wefindEigenvalues:§3.3solutionsofthefreepar190§3.3solutionsofthefreeparticleEigenstates:§3.3solutionsofthefreepar191§3.3solutionsofthefreeparticle§3.3solutionsofthefreepar192§3.3solutionsofthefreeparticleDiracholetheoryDiracseaHole:(+Ep>0,+m>0,+e>0)(positron)1932,Andersondiscoveredpositronfromcosmicrayusingcloudchamber§3.3solutionsofthefreepar193§3.4DiracequationinthecentralforcefieldEquationinnon-relativisticlimit§3.4Diracequationinthecen194§3.4Diracequationinthecentralforcefield§3.4Diracequationinthecen195§3.4Diracequationinthecentralforcefield§3.4Diracequationinthecen196§3.4DiracequationinthecentralforcefieldInnon-relativisticapproximation§3.4Diracequationinthecen197§3.4Diracequationinthecentralforcefield§3.4Diracequationinthecen198§3.4Diracequationinthecentralforcefield§3.4Diracequationinthecen199§3.4Diracequationinthecentralforcefield§3.4Diracequationinthecen200§3.4DiracequationinthecentralforcefieldNoting:uptotheorderNormalizationconditionmustbeensured§3.4Diracequationinthecen201§3.4Diracequationinthecentralforcefield§3.4Diracequationinthecen202§3.4Diracequationinthecentralforcefield§3.4Diracequationinthecen203§3.4Diracequationinthecentralforcefield§3.4Diracequationinthecen204§3.4Diracequationinthecentralforcefield§3.4Diracequationinthecen205§3.4DiracequationinthecentralforcefieldByusing§3.4Diracequationinthecen206§3.4DiracequationinthecentralforcefieldRelativisticcorrectionofkineticenergy§3.4Diracequationinthecen207§3.4DiracequationinthecentralforcefieldThomastermDarwinterm§3.4Diracequationinthecen208§3.4Diracequationinthecentralforcefield§3.4Diracequationinthecen209§3.4DiracequationinthecentralforcefieldQuantumnumberK§3.4Diracequationinthecen210§3.4Diracequationinthecentralforcefield§3.4Diracequationinthecen211§3.4Diracequationinthecentralforcefield§3.4Diracequationinthecen212§3.4Diracequationinthecentralforcefield§3.4Diracequationinthecen213§3.4Diracequationinthecentralforcefield§3.4Diracequationinthecen214§3.4Diracequationinthecentralforcefield§3.4Diracequationinthecen215§3.4Diracequationinthecentralforcefield§3.4Diracequationinthecen216§3.4Diracequationinthecentralforcefield§3.4Diracequationinthecen217§3.4Diracequationinthecentralforcefield§3.4Diracequationinthecen218§3.4DiracequationinthecentralforcefieldRadialequations§3.4Diracequationinthecen219§3.4Diracequationinthecentralforcefield§3.4Diracequationinthecen220§3.4Diracequationinthecentralforcefield§3.4Diracequationinthecen221§3.4Diracequationinthecentralforcefield§3.4Diracequationinthecen222§3.4DiracequationinthecentralforcefieldWetake§3.4Diracequationinthecen223§3.5SolutionoftheDiracequationintheCoulombfieldMotivationDiscussiontheHydrogenatomFinestructure§3.5SolutionoftheDiracequ224§3.5SolutionoftheDiracequationintheCoulombfield§3.5SolutionoftheDiracequ225§3.5SolutionoftheDiracequationintheCoulombfield§3.5SolutionoftheDiracequ226§3.5SolutionoftheDiracequationintheCoulombfield§3.5SolutionoftheDiracequ227§3.5SolutionoftheDiracequationintheCoulombfield§3.5SolutionoftheDiracequ228§3.5SolutionoftheDiracequationintheCoulombfield§3.5SolutionoftheDiracequ229§3.5SolutionoftheDiracequationintheCoulombfieldn’=0,1,2,…,n=1,2,3…§3.5SolutionoftheDiracequ230§3.5SolutionoftheDiracequationintheCoulombfield§3.5SolutionoftheDiracequ231§3.5SolutionoftheDiracequationintheCoulombfieldGroundstate1S1/2(n=0,κ=-1,n=1,j=1/2)§3.5SolutionoftheDiracequ232§3.5SolutionoftheDiracequationintheCoulombfield§3.5SolutionoftheDiracequ233§3.5SolutionoftheDiracequationintheCoulombfield§3.5SolutionoftheDiracequ234§3.5SolutionoftheDiracequationintheCoulombfieldQuestionDiraceq+non-relativisticlimitScheqZ≥137?NolimitforZUniformchargedsphere?NolimitforZFinestructureEnjEnforScheq§3.5SolutionoftheDiracequ235§3.6KleinparadoxAnotherquestionforthenon-relativisticlimitofDiracequationDoespositronexistScalarlikepotentialandvectorlikepotential§3.6KleinparadoxAnotherques236§3.6Kleinparadox§3.6Kleinparadox237§3.6Kleinparadox§3.6Kleinparadox238§3.6KleinparadoxAttheinfinity,thewavefunctionisnotzero,whichmeansthatthereisonlythescatteringstatesolutioninsteadofboundstatesolution§3.6KleinparadoxAttheinfin239§3.6KleinparadoxDiracequ