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Modern Quantum Mechanics


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Table of Contents

1. Fundamental Concepts1.1. The Stern-Gerlach Experiment1.2. Kets, Bras, and Operators1.3. Base Kets and Matrix Representations1.4. Measurements, Observaables, and the Uncertainty Relations1.5. Change of Basis1.6. Position, Momentum, and Translation1.7. Wave Functions in Position and Momentum Space 2. Quantum Dynamics 2.1. Time Evolution and the SchroeDinger Equation2.2. The SchroeDinger Versus the Heisenberg Picture2.3. Simple Harmonic Oscillator2.4. SchroeDinger's Wave Equation2.5. Elementary Solutions to SchroeDinger's Wave Equation2.6. Propogators and Feynman Path Integrals2.7. Potentials and Gauge Transformations 3. Theory of Angular Momentum3.1. Rotations and Angular Momentum Commutation Relations3.2. Spin 13.3. SO(e), SU(2), and Euler Rotations3.4. Density Operators and Pure Versus Mixed Ensembles3.5 Eigenvalues and Eigenstates of Angular Momentum3.6. Orbital Angular Momentum3.7. SchroeDinger's Equation for Central Potentials3.8 Addition of Angular Momenta3.9. Schwinger's Oscillator Model of Angular Momentum3.10. Spin Correlation Measurements and Bell's Inequality3.11. Tensor Operators 4. Symmetry in Quantum Mechanics 4.1. Symmetries, Conservation Laws, and Degeneracies4.2. Discrete Symmetries, Parity, or Space Inversion4.3. Lattice Translation as a Discrete Symmetry4.4. The Time-Reversal Discrete Symmetry 5. Approximation Methods5.1. Time-Independent Perturbation Theory: Nondegenerate Case5.2. Time-Independent Perturbation Theory: The Degenerate Case5.3. Hydrogenlike Atoms: Fine Structure and the Zeeman Effect5.4. Variational Methods5.5. Time-Depedent Potentials: The Interaction Picture5.6. Hamiltonians with Extreme Time Dependence5.7. Time-Dependent Perturbation Theory5.8. Applications to Interactions with the Classical Radiation Field5.9 Energy Shift and Decay Width 6. Scattering Theory6.1. Scattering as a Time-Dependent Perturbation6.2 The Scattering Amplitude6.3. The Born Approximation6.4. Phase Shifts and Partial Waves6.5. Eikonal Approximation6.6. Low-Energy Scattering and Bound States6.7. Resonance Scattering6.8. Symmetry Considerations in Scattering6.9 Inelastic Electron-Atom Scattering 7. Identical Particles7.1. Permutation Symmetry7.2. Symmetrization Postulate7.3. Two-Electron System7.4. The Helium Atom7.5. Multi-Particle States7.6. Quantization of the Electromagnetic Field 8. Relativistic Quantum Mechanics 3318.1. Paths to Relativisitic Quantum Mechanics8.2. The Dirac Equation8.3. Symmetries of the Dirac Equation8.4. Solving with a Central Potential8.5. Relativistic Quantum Field Theory AppendicesA. Electromagnetic Units A.1. Coulomb's Law, Charge, and CurrentA.2. Converting Between SystemsB. Brief Summary of Elementary Solutions to ShroeDinger's Wave EqationB.1. Free Particles (V=0)B.2. Piecewise Constatn Potentials in One DimensionB.3. Transmission-Reflection ProblemsB.4. Simple Harmonic OscillatorB.5. The Central Force Problem (Spherically Symmetrical Potential V=V(r)]B.6. Hydrogen Atom

About the Author

The late J.J. Sakurai, noted theorist in particle physics, was born in Tokyo, Japan in 1933. He received his B.A. from Harvard University in 1955 and his PhD from Cornell University in 1958. He was appointed as an assistant professor at the University of Chicago, where he worked until he became a professor at the University of California, Los Angeles in 1970. Sakurai died in 1982 while he was visiting a professor at CERN in Geneva, Switzerland.Jim Napolitano earned an undergraduate Physics degree at Rensselaer Polytechnic Institute in 1977, and a PhD in Physics from Stanford University in 1982. Since that time, he has conducted research in experimental nuclear and particle physics, with an emphasis on studying fundamental interactions and symmetries. He joined the faculty at Rensselaer in 1992 after working as a member of the scientific staff at two different national laboratories. He is author and co-author of over 150 scientific papers in refereed journals. Professor Napolitano maintains a keen interest in science education in general, and in particular physics education at both the undergraduate and graduate levels. He has published a textbook, co-authored with Adrian Melissinos, on Experiments in Modern Physics. Prior to his work on Modern Quantum Mechanics,Second Edition, he has taught both graduate and upper-level undergraduate courses in Quantum Mechanics, as well as an advanced graduate course in Quantum Field Theory.

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