Quantum Theory (eBook)

Professor Dr. Edouard B. Manoukian did his graduate studies at McGill and at the University of Toronto in Canada, receiving his M.Sc. and Ph.D. degrees in 1968 and 1971, respectively. He carried out research at the Theoretical Physics Institute of the University of Alberta, the Dublin Institute for Advanced Studies, and the Centre de Recherches Mathématiques Appliquées of the University of Montreal. In 1978 he joined the staff of the Department of National Defence of the Royal Military College of Canada and was appointed as a full professor in 1985. Presently E.B. Manoukian is a professor in the School of Physics of the Suranaree University of Technology. He has authored several books including the one entitled "Renormalization" (ISBN: 0124694500, New York: Academic Press, 1983) which may be of interest to readers of the present book, and he has published over 160 research papers on most aspects of theoretical physics.

Preface. Acknowledgments. 1: Fundamentals. 1.1 Selective Measurements 1.2. A, B, C to Probabilities. 1.3. Expectation Values and Matrix Representations. 1.4. Generation of States, Inner-Product Spaces, Hermitian Operators and the Eigenvalue Problem. 1.5. Pure Ensembles and Mixtures 1.6. Polarization of Light: An Interlude. 1.7. The Hilbert Space; Rigged Hilbert Space. 1.8. Self-Adjoint Operators and Their Spectra.1.9. Wigner’s Theorem on Symmetry Transformations. 1.10. Probability, Conditional Probability and Measurement. Problems. 2: Symmetries and Transformations. 2.1. Galilean Space-Time Coordinate Transformations. 2.2. Successive Galilean Transformations and the Closed Path. 2.3. Quantum Galilean Transformations and Their Generators. 2.4. The Transformation Function (x p). 2.5. Quantum Dynamics and Construction of Hamiltonians. Appendix to §2.5: Time-Evolution for Time-Dependent Hamiltonians. 2.6. Discrete Transformations: Parity and Time Reversal. 2.7. Orbital Angular Momentum and Spin. 2.8. Spinors and Arbitrary Spins. Appendix to §2.8: Transformation Rule of a Spinor of Rank One Under a Coordinate Rotation. 2.9. Supersymmetry. Problems. 3: Uncertainties, Localization, Stability and Decay of Quantum Systems. 3.1. Uncertainties, Localization and Stability. 3.2. Boundedness of the Spectra of Hamiltonians From Below. 3.3. Boundedness of Hamiltonians From Below: General Classes of Interactions. 3.4. Boundedness of Hamiltonian From Below: Multi-Particle Systems. 3.5. Decay of Quantum Systems. Appendix to §3.5: The Paley-Wiener Theorem. Problems. 4: Spectra of Hamiltonians. 4.1. Hamiltonians with Potentials Vanishing at Infinity. 4.2. On Bound-States. 4.3. Hamiltonians with Potentials Approaching Finite Constants at Infinity. 4.4. Hamiltonians with Potentials Increasing with No Bound at Infinity. 4.5. Counting the Number of Eigenvalues. Appendix to §4.5: Evaluation of Certain Integrals. 4.6. Lower Bounds to the Expectation Value of the KineticEnergy: An Application of Counting Eigenvalues. 4.7. The Eigenvalue Problem and Supersymmetry. Problems. 5: Angular Momentum Gymnastics. 5.1. The Eigenvalue Problem. 5.2. Matrix Elements of Finite Rotations. 5.3. Orbital Angular Momentum. 5.4. Spin. 5.5. Addition of Angular Momenta. 5.6. Explicit Expression for the Clebsch-Gordan Coefficients. 5.7. Vector Operators. 5.8. Tensor Operators. 5.9. Combining Several Angular Momenta: 6-j and 9-j Symbols. 5.10. Particle States and Angular Momentum; Helicity States. Problems. 6: Intricacies of Harmonic Oscillators. 6.1. The Harmonic Oscillator. 6.2 Transition to and Between Excited States in the Presence of a Time-Dependent Disturbance. 6.3. The Harmonic Oscillator in the Presence of a Disturbance at Finite Temperature. 6.4. The Fermi Oscillator. 6.5. Bose-Fermi Oscillators and Supersymmetric Bose-Fermi Transformations. 6.6. Coherent State of the Harmonic Oscillator. Problems. 7: Intricacies of the Hydrogen Atom. 7.1. Stability of the Hydrogen Atom. 7.2. The Eigenvalue Problem. 7.3. The Eigenstates. 7.4. The Hydrogen Atom Including Spin and Relativistic Corrections. Appendix to §7.4: Normalization of the Wavefunction Including Spin and Relativistic Corrections. 7.5. The Fine-Structure of the Hydrogen Atom. Appendix to §7.5: Combining Spin and Angular Momentum in the Atom. 7.6. The Hyperfine-Structure of the Hydrogen Atom. 7.7. The Non-Relativistic Lamb Shift. Appendix to §7.7: Counter-Terms and Mass Renormalization. 7.8. Decay of Excited States. 7.9. The Hydrogen Atom in External Electromagnetic Fields. Problems. 8: Quantum Physics of Spin 1/2 and Two-Level Systems; Quantum Predictions Using Such Systems. 8.1. General Properties of Spin 1/2 and Two-Level Systems. 8.2. The Pauli Hamiltonian; Supersymmetry. 8.3. Landau Levels; Expression for the g-Factor. 8.4. Spin Precession and Radiation Losses. 8.5. Anomalous Magnetic Moment of the Electron. 8.6. Density Operators and Spin. 8.7 Quantum Interference and