Principles of Quantum Mechanics

Description

A pdf of the ebook w/ metadata Cover Page Copyright Page Dedication Page Contents 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 ℏ’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 + dẋ + exẋ 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. Translational Invariance in Quantum Theory 11.2. Time Translational Invariance 11.3. Parity Invariance 11.4. 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. The Hydrogen 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 Appendix A.1. Matrix Inversion A.2. Gaussian Integrals A.3. Complex Numbers A.4. The iε Prescription Answers to Selected Exercises Table of Constants