## Table of Contents

1. Fundamental Concepts

1.1. The Stern-Gerlach Experiment

1.2. Kets, Bras, and Operators

1.3. Base Kets and Matrix Representations

1.4. Measurements, Observaables, and the Uncertainty Relations

1.5. Change of Basis

1.6. Position, Momentum, and Translation

1.7. Wave Functions in Position and Momentum Space

2. Quantum Dynamics

2.1. Time Evolution and the SchröDinger Equation

2.2. The SchröDinger Versus the Heisenberg Picture

2.3. Simple Harmonic Oscillator

2.4. SchröDinger's Wave Equation

2.5. Elementary Solutions to SchröDinger's Wave Equation

2.6. Propogators and Feynman Path Integrals

2.7. Potentials and Gauge Transformations

3. Theory of Angular Momentum

3.1. Rotations and Angular Momentum Commutation Relations

3.2. Spin 1

3.3. SO(e), SU(2), and Euler Rotations

3.4. Density Operators and Pure Versus Mixed Ensembles

3.5 Eigenvalues and Eigenstates of Angular Momentum

3.6. Orbital Angular Momentum

3.7. SchröDinger's Equation for Central Potentials

3.8 Addition of Angular Momenta

3.9. Schwinger’s Oscillator Model of Angular Momentum

3.10. Spin Correlation Measurements and Bell’s Inequality

3.11. Tensor Operators

4. Symmetry in Quantum Mechanics

4.1. Symmetries, Conservation Laws, and Degeneracies

4.2. Discrete Symmetries, Parity, or Space Inversion

4.3. Lattice Translation as a Discrete Symmetry

4.4. The Time-Reversal Discrete Symmetry

5. Approximation Methods

5.1. Time-Independent Perturbation Theory: Nondegenerate Case

5.2. Time-Independent Perturbation Theory: The Degenerate Case

5.3. Hydrogenlike Atoms: Fine Structure and the Zeeman Effect

5.4. Variational Methods

5.5. Time-Depedent Potentials: The Interaction Picture

5.6. Hamiltonians with Extreme Time Dependence

5.7. Time-Dependent Perturbation Theory

5.8. Applications to Interactions with the Classical Radiation Field

5.9 Energy Shift and Decay Width

6. Scattering Theory

6.1. Scattering as a Time-Dependent Perturbation

6.2 The Scattering Amplitude

6.3. The Born Approximation

6.4. Phase Shifts and Partial Waves

6.5. Eikonal Approximation

6.6. Low-Energy Scattering and Bound States

6.7. Resonance Scattering

6.8. Symmetry Considerations in Scattering

6.9 Inelastic Electron-Atom Scattering

7. Identical Particles

7.1. Permutation Symmetry

7.2. Symmetrization Postulate

7.3. Two-Electron System

7.4. The Helium Atom

7.5. Multi-Particle States

7.6. Quantization of the Electromagnetic Field

8. Relativistic Quantum Mechanics 331

8.1. Paths to Relativisitic Quantum Mechanics

8.2. The Dirac Equation

8.3. Symmetries of the Dirac Equation

8.4. Solving with a Central Potential

8.5. Relativistic Quantum Field Theory

Appendices

A. Electromagnetic Units

A.1. Coulomb’s Law, Charge, and Current

A.2. Converting Between Systems

B. Brief Summary of Elementary Solutions to ShröDinger's Wave Eqation

B.1. Free Particles (V=0)

B.2. Piecewise Constatn Potentials in One Dimension

B.3. Transmission–Reflection Problems

B.4. Simple Harmonic Oscillator

B.5. The Central Force Problem (Spherically Symmetrical Potential V=V(r)]

B.6. Hydrogen Atom