Quantum

1. Particles and Waves.- 1. Generalized Coordinates.- 2. Energy Conservation.- 3. Principle of Virtual Work.- 4. Lagrange Equations.- 5. Hamilton's Principle of Least Action.- 6. Conservation Laws.- 7. The Center of Gravity Theorem.- 8. Symmetry and Invariance.- 9. Hamilton's Equations.- 10. Maupertuis' Least-Action Principle.- 11. Canonical Transformations.- 12. Poisson's Equations.- 13. Hamilton-Jacobi Equations.- 14. Propagation Equation of Geometric Optics.- 15. Mechanics and Waves.- 16. Wave Mechanics.- 17. Analytical Mechanics - Schematic Summary.- 2. Wave Mechanics.- 1. Conservative Systems.- 2. Interpretations of the Wave Function.- 3. Mean Values of Observables.- 4. Heisenberg's Uncertainty Relation.- 5. Interpretations of Wave Mechanics.- 6. Wave Mechanics - Schematic Summary.- 3. One-Dimensional Systems.- 1. Motion of the Center of Mass.- 2. General Properties of the Wave Function.- 3. Stationary Schrödinger Equation.- 4. Semi-classical (W.K.B.) Approximation.- 4. Dirac Formalism.- 1. Postulates of Quantum Mechanics.- 2. Dirac Formalism.- 3. Observables.- 4. Complete Set of Compatible Observables.- 5. Heisenberg's Uncertainty Relations.- 6. Dirac Formalism - Schematic Summary.- 5. Representations.- 1. Wave Mechanics.- 2. Matrix Mechanics.- 3. Wave Mechanics - Schematic Summary.- 4. Matrix Mechanics - Schematic Summary.- 6. Quantum Dynamics.- 1. Time-Evolution Operator.- 2. Two Different Descriptions of Quantum Dynamics.- 3. The Correspondence Principle.- 4. Intermediate Description.- 5. Interpretation of Decoherence in Quantum Mechanics.- 6. Quantum Dynamics - Schematic Summary.- 7. Path Integrals.- 1. Evolution of the Wave Function.- 2. Path Integrals.- 3. Equivalence to the Schrödinger Equation.- 4. Action in Quantum Physics.- 5. Quantum Paths and Fractals.- 6. Path Integrals - Schematic Summary.- 8. Symmetries and Invariances.- 1. Unitary Transformations.- 2. Anti-unitary Transformations.- 3. Gauge Transformations.- 9. Angular Momentum.- 1. General Definition.- 2. Standard Representation.- 3. Examples of Angular Momenta.- 4. Magnetic Moments.- 10. Addition Theorems.- 1. Coupling of Two Angular Momenta.- 2. Clebsch-Gordan Coefficients.- 3. 3jm Coefficients.- 4. Coupling of n Angular Momenta.- 5. Change of Coupling Mode.- 6. Introduction to the Graphical Method.- Appendix 1: Table of Selected 3jm and 6j Coefficients.- Appendix 2: Diquark.- 11. Rotations.- 1. Introduction.- 2. Infinitesimal Rotations.- 3. Finite Rotations.- 4. Standard Representation.- 5. Fundamental Theorem of Pinch.- 6. Transformation Rules of Graphical Spin Algebra.- 12. Spherical Harmonics.- 1. Orbital Angular Momentum.- 2. Spherical Harmonic Y?o.- 3. General Statement.- 4. Parity.- 5. Orthonormalization and Closure.- 6. Graphical Representation.- 7. Integration of Three Spherical Harmonics.- 8. Contraction.- 9. Addition Theorem.- 10. Coupled Spherical Harmonics.- 11. Solid Spherical Harmonics.- 12.Schrödinger Equation in a Central Potential.- 13. Irreducible Tensor Operators.- 1. Definitions.- 2. Graphical Representation.- 3. Hermitian Conjugate.- 4. Scalar Product.- 5. Tensor Product.- 6. Standardization of a Vector Operator.- 7. Wigner-Eckart Theorem.- 8. Magnetic Moments.- 9. Density Operator.- 10. Differential Operators.- 11. Irreducible Tensor Operators - Schematic Summary.- Appendix 1: Reduced Matrix Elements.- Appendix 2: Graphical Vector Analysis.- 14. Perturbations.- 1. Stationary Perturbations.- 2. Variational Method.- 3. Time-Dependent Perturbations.- 15. Scattering of Particles.- 1. Scattering Operator.- 2. Transition Operator.- 3. Differential Cross Section.- 4. Scattering Amplitude and Interaction Potential.- 5. Lippmann-Schwinger Equations.- 6. Phase-Shift Method.- 7. Angular Distribution and Polarization.- 8. Scattering of Particles - Schematic Summary.- 16. Second Quantization.- 1. One-Dimensional Harmonic Oscillator.- 2. The p-Dimensional Harmonic Oscillator.- 3. Bosons and Fermions.- 4. Fermion Systems.- 5. Boson Systems.- 6. Simple Harmonic Oscillator - Schematic Summary.- 7. Second Quantization - Schematic Summary.- Appendix: The q-Commutators.- 17. Boson Fields.- 1. Classical Field Theory.- 2. Massive Scalar Fields.- 3. Higgs Fields.- 4. The Electromagnetic Field.- 5. Quantization of a Boson Field.- 18. Fermion Fields.- 1. Dirac Equation of a Free Particle.- 2. Dirac ? Matrices.- 3. The Adjoint Dirac Equation.- 4. Lagrangian Density and Field Equations.- 5. Probability Density.- 6. Gauge Invariance and Noether's Theorem.- 7. Interaction with the Electromagnetic Field.- 8. Local Gauge Invariance.- 9. Electron Spin.- 10. Solutions for a Free Electron.- 11. Charge Conjugation.- 12. Hydrogen Atom.- 13. Coulomb Elastic Scattering.- 14. Quantization of a Fermion Field.- 15. Dirac Equation - Schematic Summary.- 19. Quantum X-Dynamics.- 1. Quantum Electrodynamics.- 2. Elementary Introduction to Quantum Chromodynamics.- 3. The GSW Standard Model.- 4. Grand Unification Theories.- Appendix: Introduction to Supersymmetry.- 20. Quantum Cosmology.- 1. Introduction.- 2. Essentials of General Relativity.- 3. The Correspondence Principle.- 4. Essentials of the Standard Model of Cosmology.- 5. Hamiltonian Statement of Einstein Equations.- 6. Fundamental Equation of Quantum Cosmology.- 7. Quantization in the Mini-Superspaces.- Exercises.- References.- Author Index.