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1. Mathematical Introduction.-
1.1. Linear Vector Spaces: Basics.-
1.2. Inner Product Spaces.-
1.3. Dual Spaces and the Dirac Notation.-
1.4. Subspaces.-
1.5. Linear Operators.-
1.6. Matrix Elements of Linear Operators.-
1.7. Active and Passive Transformations.-
1.8. The Eigenvalue Problem.-
1.9. Functions of Operators and Related Concepts.-
1.10. Generalization to Infinite Dimensions.-
2. Review of Classical Mechanics.-
2.1. The Principle of Least Action and Lagrangian Mechanics.-
2.2. The Electromagnetic Lagrangian.-
2.3. The Two-Body Problem.-
2.4. How Smart Is a Particle?.-
2.5. The Hamiltonian Formalism.-
2.6. The Electromagnetic Force in the Hamiltonian Scheme.-
2.7. Cyclic Coordinates, Poisson Brackets, and Canonical Transformations.-
2.8. Symmetries and Their Consequences.-
3. All Is Not Well with Classical Mechanics.-
3.1. Particles and Waves in Classical Physics.-
3.2. An Experiment with Waves and Particles (Classical).-
3.3. The Double-Slit Experiment with Light.-
3.4. Matter Waves (de Broglie Waves).-
3.5. Conclusions.-
4. The Postulates--a General Discussion.-
4.1. The Postulates.-
4.2. Discussion of Postulates I -III.-
4.3. The Schrödinger Equation (Dotting Your i''s and Crossing your ?''s).-
5. Simple Problems in One Dimension.-
5.1. The Free Particle.-
5.2. The Particle in a Box.-
5.3. The Continuity Equation for Probability.-
5.4. The Single-Step Potential: a Problem in Scattering.-
5.5. The Double-Slit Experiment.-
5.6. Some Theorems.-
6. The Classical Limit.-
7. The Harmonic Oscillator.-
7.1. Why Study the Harmonic Oscillator?.-
7.2. Review of the Classical Oscillator.-
7.3. Quantization of the Oscillator (Coordinate Basis).-
7.4. The Oscillator in the Energy Basis.-
7.5. Passage from the Energy Basis to the X Basis.-
8. The Path Integral Formulation of Quantum Theory.-
8.1. The Path Integral Recipe.-
8.2. Analysis of the Recipe.-
8.3. An Approximation to U(t) for the Free Particle.-
8.4. Path Integral Evaluation of the Free-Particle Propagator.-
8.5. Equivalence to the Schrödinger Equation.-
8.6. Potentials of the Form V=a + bx + cx2 + d? + ex?.-
9. The Heisenberg Uncertainty Relations.-
9.1. Introduction.-
9.2. Derivation of the Uncertainty Relations.-
9.3. The Minimum Uncertainty Packet.-
9.4. Applications of the Uncertainty Principle.-
9.5. The Energy-Time Uncertainty Relation.-
10. Systems with N Degrees of Freedom.-
10.1. N Particles in One Dimension.-
10.2. More Particles in More Dimensions.-
10.3. Identical Particles.-
11. Symmetries and Their Consequences.-
11.1. Overview.-
11.2. Translational Invariance in Quantum Theory.-
11.3. Time Translational Invariance.-
11.4. Parity Invariance.-
11.5. Time-Reversal Symmetry.-
12. Rotational Invariance and Angular Momentum.-
12.1. Translations in Two Dimensions.-
12.2. Rotations in Two Dimensions.-
12.3. The Eigenvalue Problem of Lz.-
12.4. Angular Momentum in Three Dimensions.-
12.5. The Eigenvalue Problem of L2 and Lz.-
12.6. Solution of Rotationally Invariant Problems.-
13. TheHydrogen Atom.-
13.1. The Eigenvalue Problem.-
13.2. The Degeneracy of the Hydrogen Spectrum.-
13.3. Numerical Estimates and Comparison with Experiment.-
13.4. Multielectron Atoms and the Periodic Table.-
14. Spin.-
14.1. Introduction.-
14.2. What is the Nature of Spin?.-
14.3. Kinematics of Spin.-
14.4. Spin Dynamics.-
14.5. Return of Orbital Degrees of Freedom.-
15. Addition of Angular Momenta.-
15.1. A Simple Example.-
15.2. The General Problem.-
15.3. Irreducible Tensor Operators.-
15.4. Explanation of Some "Accidental" Degeneracies.-
16. Variational and WKB Methods.-
16.1. The Variational Method.-
16.2. The Wentzel-Kramers-Brillouin Method.-
17. Time-Independent Perturbation Theory.-
17.1. The Formalism.-
17.2. Some Examples.-
17.3. Degenerate Perturbation Theory.-
18. Time-Dependent Perturbation Theory.-
18.1. The Problem.-
18.2. First-Order Perturbation Theory.-
18.3. Higher Orders in Perturbation Theory.-
18.4. A General Discussion of Electromagnetic Interactions.-
18.5. Interaction of Atoms with Electromagnetic Radiation.-
19. Scattering Theory.-
19.1. Introduction.-
19.2. Recapitulation of One-Dimensional Scattering and Overview.-
19.3. The Born Approximation (Time-Dependent Description).-
19.4. Born Again (The Time-Independent Approximation).-
19.5. The Partial Wave Expansion.-
19.6. Two-Particle Scattering.-
20. The Dirac Equation.-
20.1. The Free-Particle Dirac Equation.-
20.2. Electromagnetic Interaction of the Dirac Particle.-
20.3. More on Relativistic Quantum Mechanics.-
21. Path Integrals--II.-
21.1. Derivation of the Path Integral.-
21.2. Imaginary Time Formalism.-
21.3. Spin and Fermion Path Integrals.-
21.4. Summary.- A.l. Matrix Inversion.- A.2. Gaussian Integrals.- A.3. Complex Numbers.