Advanced Quantum Mechanics

1. Introduction. 1.1. Books. 1.2. Subject matter. 1.3. Detailed program. 1.4. One-particle theories -- 2. The Dirac theory. 2.1. The form of the Dirac equation. 2.2. Lorentz invariance of the Dirac equation. 2.3. To find the S. 2.4. The covariant notation. 2.5. Conservation laws. Existence of spin. 2.6. Elementary solutions. 2.7. The hole theory. 2.8. Positron states. 2.9. Electromagnetic properties of the electron. 2.10. The hydrogen atom. 2.11. Solution of radial equation. 2.12. Behaviour of an electron in a non-relativistic approximation. 2.13. Summary of matrices in the Dirac theory in our notation. 2.14. Summary of matrices in the Dirac theory in the Feynman notation -- 3. Scattering problems and born approximation. 3.1. General discussion. 3.2. Projection operators. 3.3. Calculation of traces. 3.4. Scattering of two electrons in born approximation. The Moller formula. 3.5. Relation of cross-sections to transition amplitudes. 3.6. Results for Moller scattering. 3.7. Note on the treatment of exchange effects. 3.8. Relativistic Treatment of Several Particles -- 4. Field theory. 4.1. Classical relativistic field theory. 4.2. Quantum relativistic field theory. 4.3. The Feynman method of quantization. 4.4. The Schwinger action principle -- 5. Examples of Quantized Field Theories. 5.1. The Maxwell field. 5.2. Theory of line shift and line width. 5.3. Field theory of the Dirac electron, without interaction. 5.4. Field theory of Dirac electron in external field. 5.5. Field theory of Dirac and Maxwell fields -- 6. Free particle scattering problems. 6.1. Moller scattering of two electrons. 6.2. Scattering of a photon by an electron. The Compton effect. Klein-Nishina formula. 6.3. Two quantum pair annihilation. 6.4. Bremsstrahlung and pair creation in the Coulomb field of an atom -- 7. General theory of free particle scattering. 7.1. The reduction of an operator to normal form. 7.2. Feynman graphs. 7.3. Feynman rules of calculation. 7.4. The self-energy of the electron. 7.5. Second-order radiative corrections to scattering. 7.6. The treatment of low-frequency photons. The infra-red catastrophe -- 8. Scattering by a static potential. Comparison with experimental results. 8.1. The magnetic moment of the electron. 8.2. Relativistic calculation of the lamb shift