Table of Contents
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
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