苏汝铿高等量子力学讲义(英文版)Chapter3 Relativistic.ppt

Chapter3RelativisticQuantumMechanics Introduction Non relativisticquantummechanics relativisticquantummechanicsSchr dingerequation Klein GordonequationS integerDiracequationS halfintegerSpinisautomaticallycontainedinDiracequation 3 1Klein Gordonequation Lorentztransormation time spaceareofthesameweightK Gequation 3 1Klein Gordonequation 3 1Klein Gordonequation 3 1Klein Gordonequation 3 1Klein Gordonequation DiscussionNegativeenergy instable 3 1Klein Gordonequation Negativeprobability 3 1Klein Gordonequation 3 1Klein Gordonequation Non relativisticlimit K Geq Scheq 3 1Klein Gordonequation 3 1Klein Gordonequation 3 1Klein Gordonequation Withelectromagneticfield 3 1Klein Gordonequation 3 1Klein Gordonequation Covariantform 3 1Klein Gordonequation 3 1Klein Gordonequation 3 1Klein Gordonequation 3 2Diracequation Howtoovercomethenegativeprobabilitydifficulty 3 2Diracequation 3 2Diracequation 3 2Diracequation 3 2Diracequation Theconditionfor and 1 Theymustfollowtherelation2 OperatorHmustbeHermitian3 Lorentzinvariance 3 2Diracequation 3 2Diracequation 3 2Diracequation 3 2Diracequation 4anti commutematrices and 4 4matrices 3 2Diracequation 3 2Diracequation Conservationlawoftheprobabilityflux 3 2Diracequation 3 2Diracequation 3 3solutionsofthefreeparticle 3 3solutionsofthefreeparticle 3 3solutionsofthefreeparticle 3 3solutionsofthefreeparticle 3 3solutionsofthefreeparticle 3 3solutionsofthefreeparticle 3 3solutionsofthefreeparticle 3 3solutionsofthefreeparticle 3 3solutionsofthefreeparticle DiscussionPositiveenergystate 1 Negativeenergystate 1 Eigenstatesofmomentump 3 3solutionsofthefreeparticle Orbitalangularmomentumisnotconserved 3 3solutionsofthefreeparticle 3 3solutionsofthefreeparticle Spinangularmomentum Or 3 3solutionsofthefreeparticle 3 3solutionsofthefreeparticle 3 3solutionsofthefreeparticle 3 3solutionsofthefreeparticle Helicityoperator 3 3solutionsofthefreeparticle 3 3solutionsofthefreeparticle If wefind Eigenvalues 3 3solutionsofthefreeparticle Eigenstates 3 3solutionsofthefreeparticle 3 3solutionsofthefreeparticle Diracholetheory DiracseaHole Ep 0 m 0 e 0 positron 1932 Andersondiscoveredpositronfromcosmicrayusingcloudchamber 3 4Diracequationinthecentralforcefield Equationinnon relativisticlimit 3 4Diracequationinthecentralforcefield 3 4Diracequationinthecentralforcefield 3 4Diracequationinthecentralforcefield Innon relativisticapproximation 3 4Diracequationinthecentralforcefield 3 4Diracequationinthecentralforcefield 3 4Diracequationinthecentralforcefield 3 4Diracequationinthecentralforcefield Noting uptotheorderNormalizationconditionmustbeensured 3 4Diracequationinthecentralforcefield 3 4Diracequationinthecentralforcefield 3 4Diracequationinthecentralforcefield 3 4Diracequationinthecentralforcefield 3 4Diracequationinthecentralforcefield Byusing 3 4Diracequationinthecentralforcefield Relativisticcorrectionofkineticenergy 3 4Diracequationinthecentralforcefield Thomasterm Darwinterm 3 4Diracequationinthecentralforcefield 3 4Diracequationinthecentralforcefield QuantumnumberK 3 4Diracequationinthecentralforcefield 3 4Diracequationinthecentralforcefield 3 4Diracequationinthecentralforcefield 3 4Diracequationinthecentralforcefield 3 4Diracequationinthecentralforcefield 3 4Diracequationinthecentralforcefield 3 4Diracequationinthecentralforcefield 3 4Diracequationinthecentralforcefield 3 4Diracequationinthecentralforcefield Radialequations 3 4Diracequationinthecentralforcefield 3 4Diracequationinthecentralforcefield 3 4Diracequationinthecentralforcefield 3 4Diracequationinthecentralforcefield Wetake 3 5SolutionoftheDiracequationintheCoulombfield MotivationDiscussiontheHydrogenatomFinestructure 3 5SolutionoftheDiracequationintheCoulombfield 3 5SolutionoftheDiracequationintheCoulombfield 3 5SolutionoftheDiracequationintheCoulombfield 3 5SolutionoftheDiracequationintheCoulombfield 3 5SolutionoftheDiracequationintheCoulombfield 3 5SolutionoftheDiracequationintheCoulombfield n 0 1 2 n 1 2 3 3 5SolutionoftheDiracequationintheCoulombfield 3 5SolutionoftheDiracequationintheCoulombfield Groundstate1S1 2 n 0 1 n 1 j 1 2 3 5SolutionoftheDiracequationintheCoulombfield 3 5SolutionoftheDiracequationintheCoulombfield 3 5SolutionoftheDiracequationintheCoulombfield QuestionDiraceq non relativisticlimit ScheqZ 137 NolimitforZUniformchargedsphere NolimitforZFinestructureEnj EnforScheq 3 6Kleinparadox Anotherquestionforthenon relativisticlimitofDiracequationDoespositronexistScalarlikepotentialandvectorlikepotential 3 6Kleinparadox 3 6Kleinparadox 3 6Kleinparadox Attheinfinity thewavefunctionisnotzero whichmeansthatthereisonlythescatteringstatesolutioninsteadofboundstatesolution 3 6Kleinparadox 3 6Kleinparadox ThephysicsofKleinparadox 3 6Kleinparadox 3 6Kleinparadox 3 6Kleinparadox 3 6Kleinparadox 3 6Kleinparadox 3 6Kleinparadox 3 6Kleinparadox 3 6Kleinparadox 3 6Kleinparadox 3 6Kleinparadox 3 6Kleinparadox 3 6Kleinparadox 3 6Kleinparadox 3 6Kleinparadox Ifp mc 3 6Kleinparadox TheexplanationofKleinparadox 3 6Kleinparadox 3 6Kleinparadox 3 6Kleinparadox 3 6Kleinparadox 3 6Kleinparadox 3 6Kleinparadox 3 6Kleinparadox 3 6Kleinparadox 3 7MITbagmodel Motivation canweestablishamodeltoconfinequark scalarlikepotential 3 7MITbagmodel 3 7MITbagmodel 3 7