复旦量子力学讲义qmapter.ppt
Chapter 3Relativistic Quantum Mechanics,Introduction,Non-relativistic quantum mechanics relativistic quantum mechanicsSchrdinger equation Klein-Gordon equation S integerDirac equation S half integerSpin is automatically contained in Dirac equation,3.1 Klein Gordon equation,Lorentz transormation time,space are of the same weightK G equation,3.1 Klein Gordon equation,3.1 Klein Gordon equation,3.1 Klein Gordon equation,3.1 Klein Gordon equation,DiscussionNegative energy instable,3.1 Klein Gordon equation,Negative probability,3.1 Klein Gordon equation,3.1 Klein Gordon equation,Non-relativistic limit:K-G eq Sch eq,3.1 Klein Gordon equation,3.1 Klein Gordon equation,3.1 Klein Gordon equation,With electromagnetic field,3.1 Klein Gordon equation,3.1 Klein Gordon equation,Covariant form,3.1 Klein Gordon equation,3.1 Klein Gordon equation,3.1 Klein Gordon equation,3.2 Dirac equation,How to overcome the negative probability difficulty,3.2 Dirac equation,3.2 Dirac equation,3.2 Dirac equation,3.2 Dirac equation,The condition for and 1)They must follow the relation2)Operator H must be Hermitian3)Lorentz invariance,3.2 Dirac equation,3.2 Dirac equation,3.2 Dirac equation,3.2 Dirac equation,4 anti-commute matrices and 44 matrices,3.2 Dirac equation,3.2 Dirac equation,Conservation law of the probability flux,3.2 Dirac equation,3.2 Dirac equation,3.3 solutions of the free particle,3.3 solutions of the free particle,3.3 solutions of the free particle,3.3 solutions of the free particle,3.3 solutions of the free particle,3.3 solutions of the free particle,3.3 solutions of the free particle,3.3 solutions of the free particle,3.3 solutions of the free particle,DiscussionPositive energy state(=+1)Negative energy state(=-1)Eigenstates of momentum p,3.3 solutions of the free particle,Orbital angular momentum is not conserved,3.3 solutions of the free particle,3.3 solutions of the free particle,Spin angular momentum,Or,3.3 solutions of the free particle,3.3 solutions of the free particle,3.3 solutions of the free particle,3.3 solutions of the free particle,Helicity operator,3.3 solutions of the free particle,3.3 solutions of the free particle,If,we find,Eigenvalues:,3.3 solutions of the free particle,Eigenstates:,3.3 solutions of the free particle,3.3 solutions of the free particle,Dirac hole theory Dirac seaHole:(+Ep0,+m0,+e0)(positron)1932,Anderson discovered positron from cosmic ray using cloud chamber,3.4 Dirac equation in the central force field,Equation in non-relativistic limit,3.4 Dirac equation in the central force field,3.4 Dirac equation in the central force field,3.4 Dirac equation in the central force field,In non-relativistic approximation,3.4 Dirac equation in the central force field,3.4 Dirac equation in the central force field,3.4 Dirac equation in the central force field,3.4 Dirac equation in the central force field,Noting:up to the orderNormalization condition must be ensured,3.4 Dirac equation in the central force field,3.4 Dirac equation in the central force field,3.4 Dirac equation in the central force field,3.4 Dirac equation in the central force field,3.4 Dirac equation in the central force field,By using,3.4 Dirac equation in the central force field,Relativistic correction of kinetic energy,3.4 Dirac equation in the central force field,Thomas term,Darwin term,3.4 Dirac equation in the central force field,3.4 Dirac equation in the central force field,Quantum number K,3.4 Dirac equation in the central force field,3.4 Dirac equation in the central force field,3.4 Dirac equation in the central force field,3.4 Dirac equation in the central force field,3.4 Dirac equation in the central force field,3.4 Dirac equation in the central force field,3.4 Dirac equation in the central force field,3.4 Dirac equation in the central force field,3.4 Dirac equation in the central force field,Radial equations,3.4 Dirac equation in the central force field,3.4 Dirac equation in the central force field,3.4 Dirac equation in the central force field,3.4 Dirac equation in the central force field,We take,3.5 Solution of the Dirac equation in the Coulomb field,MotivationDiscussion the Hydrogen atomFine structure,3.5 Solution of the Dirac equation in the Coulomb field,3.5 Solution of the Dirac equation in the Coulomb field,3.5 Solution of the Dirac equation in the Coulomb field,3.5 Solution of the Dirac equation in the Coulomb field,3.5 Solution of the Dirac equation in the Coulomb field,3.5 Solution of the Dirac equation in the Coulomb field,n=0,1,2,n=1,2,3,3.5 Solution of the Dirac equation in the Coulomb field,3.5 Solution of the Dirac equation in the Coulomb field,Ground state 1S1/2(n=0,=-1,n=1,j=1/2),3.5 Solution of the Dirac equation in the Coulomb field,3.5 Solution of the Dirac equation in the Coulomb field,3.5 Solution of the Dirac equation in the Coulomb field,QuestionDirac eq+non-relativistic limit Sch eq Z137?No limit for ZUniform charged sphere?No limit for ZFine structure Enj En for Sch eq,3.6 Klein paradox,Another question for the non-relativistic limit of Dirac equationDoes positron existScalarlike potential and vectorlike potential,3.6 Klein paradox,3.6 Klein paradox,3.6 Klein paradox,At the infinity,the wave function is not zero,which means that there is only the scattering state solution instead of bound state solution,3.6 Klein paradox,3.6 Klein paradox,The physics of Klein paradox,3.6 Klein paradox,3.6 Klein paradox,3.6 Klein paradox,3.6 Klein paradox,3.6 Klein paradox,3.6 Klein paradox,3.6 Klein paradox,3.6 Klein paradox,3.6 Klein paradox,3.6 Klein paradox,3.6 Klein paradox,3.6 Klein paradox,3.6 Klein paradox,3.6 Klein paradox,If p=mc,3.6 Klein paradox,The explanation of Klein paradox,3.6 Klein paradox,3.6 Klein paradox,3.6 Klein paradox,3.6 Klein paradox,3.6 Klein paradox,3.6 Klein paradox,3.6 Klein paradox,3.6 Klein paradox,3.7 MIT bag model,Motivation:can we establish a model to confine quark scalarlike potential,3.7 MIT bag model,3.7 MIT bag model,3.7 MIT bag model,Introducing scalarlike potential,3.7 MIT bag model,3.7 MIT bag model,3.7 MIT bag model,When gg we find a exponentially decaying solution,3.7 MIT bag model,Solution of step function,3.7 MIT bag model,3.7 MIT bag model,3.7 MIT bag model,3.7 MIT bag model,3.7 MIT bag model,3.7 MIT bag model,3.7 MIT bag model,
