Quantum Mechanics

Preface

Introduction

Chapter 1. Physical Basis of Quantum Theory

1.1 Particles and Waves

1.2 The Schrödinger Equation for a Particle

1.3 Probability Density and Probability Current

1.4 The Classical Limit for Motion of a Wave Packet

Chapter 2. Some Simple Solutions of Schrödinger's Equation

2.1 The Particle in a Container

2.2 The Harmonic Oscillator

2.3 The Hydrogen Atom. Atomic Units

2.4 The Free Particle

2.5 One-dimensional Step Potential with Finite Potential Height

Chapter 3. Mathematical Digression

3.1 Preliminaries. Operators and Eigenvalue Equations

3.2 Eigenfunction Expansions

3.3 Generalization to Many Variables

3.4 Linear Vector Spaces. Basic Ideas

3.5 Matrix Representation of Operators

3.6 Change of Representation

3.7 Hermitian Operators and Eigenvalue Equations in Vector Space

3.8 Composition of Vector Spaces. Product Space

Chapter 4. General Formulation of Quantum Mechanics

4.1 The Postulates

4.2 The State Vector and its Time Development

4.3 The Expectation Value Postulate

4.4 Significance of the Eigenvalue Equation

4.5 The Uncertainty Principle

4.6 Time-development and the Energy-time Uncertainty Principle

4.7 The Completeness of Eigenfunction Sets

4.8 Properties of the Operators

4.9 Electron Spin

Chapter 5. General Theory of Representations

5.1 Dirac Notation. Discrete Case

5.2 An Example. The Harmonic Oscillator

5.3 Dirac Notation. Continuous Case

5.4 Transformation Theory. The Momentum Representation

5.5 The Schrödinger Equation in Momentum Space

5.6 Time-evolution. The Heisenberg Representation

5.7 Representation of Incompletely Specified States

Appendix 1. The Schrödinger Equation in Generalized Coordinates

Appendix 2. Separation of Partial Differential Equations

Appendix 3. Series Solution of Second-order Differential Equations

Appendix 4. Projection Operators and Normal Forms

Index