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

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1、Chapter3RelativisticQuantumMechanicsIntroductionNon-relativisticquantummechanicsrelativisticquantummechanicsSchrödingerequationKlein-GordonequationS~integerDiracequationS~halfintegerSpinisautomaticallycontainedinDiracequation§3.1Klein–GordonequationLor

2、entztransormationtime,spaceareofthesameweightK–Gequation§3.1Klein–Gordonequation§3.1Klein–Gordonequation§3.1Klein–Gordonequation§3.1Klein–GordonequationDiscussionNegativeenergyinstable§3.1Klein–GordonequationNegativeprobability§3.1Klein–Gordonequation§3

3、.1Klein–GordonequationNon-relativisticlimit:K-GeqScheq§3.1Klein–Gordonequation§3.1Klein–Gordonequation§3.1Klein–GordonequationWithelectromagneticfield§3.1Klein–Gordonequation§3.1Klein–GordonequationCovariantform§3.1Klein–Gordonequation§3.1Klein–Gordonequ

4、ation§3.1Klein–Gordonequation§3.2DiracequationHowtoovercomethenegativeprobabilitydifficulty§3.2Diracequation§3.2Diracequation§3.2Diracequation§3.2DiracequationTheconditionforαandβ1)Theymustfollowtherelation2)OperatorHmustbeHermitian3)Lorentzinvariance§3.2

5、Diracequation§3.2Diracequation§3.2Diracequation§3.2Diracequation4anti-commutematricesαandβ4×4matrices§3.2Diracequation§3.2DiracequationConservationlawoftheprobabilityflux§3.2Diracequation§3.2Diracequation§3.3solutionsofthefreeparticle§3.3solutionsofthefr

6、eeparticle§3.3solutionsofthefreeparticle§3.3solutionsofthefreeparticle§3.3solutionsofthefreeparticle§3.3solutionsofthefreeparticle§3.3solutionsofthefreeparticle§3.3solutionsofthefreeparticle§3.3solutionsofthefreeparticleDiscussionPositiveenergystate(λ=+1)

7、Negativeenergystate(λ=-1)Eigenstatesofmomentump§3.3solutionsofthefreeparticleOrbitalangularmomentumisnotconserved§3.3solutionsofthefreeparticle§3.3solutionsofthefreeparticleSpinangularmomentumOr§3.3solutionsofthefreeparticle§3.3solutionsofthefreeparticle§

8、3.3solutionsofthefreeparticle§3.3solutionsofthefreeparticleHelicityoperator§3.3solutionsofthefreeparticle§3.3solutionsofthefreeparticleIf,wefindEigenvalues:§3.3solutionsofthefreeparticleEigenstates:§3.3solutionsofth