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Quantum Mechanics - 1 & 2: Quantum Mechanics - 2 (PHY-411)

Quantum mechanics is the body of scientific laws that describe the wacky behavior of photons, electrons and the other particles that make up the universe

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Course Outline

Course Contents: Relativistic description of spin-0 particles: Kelin-Gordon equation; Canonical and Lorentz covariant formulations of the Klein Gordon equation, Hamilton formulation of the Klein, Hamilton formulation of the Klein-Gordon Equation, Interpretation of negative solutions, Antiparticles.Symmetry transformations; Active and passive transformations, Lorentz transformations, Discrete transformations. One-Particle interpretation of the Klein-Gordon theory, Generalized scalar product, One-particle operatorsand Feshbach-Villars representation, Validity range of the one-particle concept, Klein paradox, Nonrelativistic approximation of the Klein-Gordon theory, Nonrelativistic limit, Relativistic corrections. Simple one-particle systems; Potential well, Radial Klein-Gordon equation, Free particle and spherically symmetric potential well, Coulomb potential, Oscillator-coulomb potential.Relativistic description of spin-1/2 particles; Dirac equation, Canonical formulation of the Dirac equation, Canonical formulation of the Dirac equation, Properties of γ-matrices and covariant bilinear forms, Spin operator, Projection operators, Interpretation of negative solutions, Antiparticlesand holetheory. Symmetry transformations; Proper Lorentz transformations, Spin of Dirac solutions, Discrete transformations. One-particle interpretation of the Dirac theory; One-particle operatorsand Feshbach-Villars Representation, Validity range of the one-particle concept, Klein paradox. Nonrelativistic approximation of the Dirac theory; Nonrelativistic limit, Relativistic corrections. Simple one-particle systems; Potential well, Radial form of the Dirac equation, Free particle and centrally symmetric potential well, Coulomb potential.Relativistic scattering theory: Review: Nonrelativistic scattering theory, Solution of the general Schr¨odingerequation, Propagator decomposition by schr¨odinger solutions, Scattering formalism, coulomb scattering.Scattering of spin-1/2 particles, Solution of the general Dirac equation, Fourier decomposition of the free Fermion propagator, Scattering formalism, Trace evaluations with γ-matrices. Spin-1/2 scattering processes;Coulomb scattering of electrons, Electron-proton scattering (I), Electron-proton scattering (II), Preliminary Feynman rules in momentum space, Electron-electron scattering, Electron-positron scattering, Compton scattering against electrons, Electron-positron annihilation, Conclusion: Feynman diagrams in momentum space. higher order corrections; Vacuum polarization, Self-energy, Vortex correction, Physical consequences. Scattering of spin-0 particles; Solution of the general Klein-Gordon equation, Scattering formalism, Coulomb scattering of pions, Pion-pion scattering, Pion production via electrons, Compton scattering against pions, Conclusion: Enhanced Feynman rulesin momentum space.

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