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Contents
Preface xi
Introduction: The Phenomena of Quantum Mechanics 1
Chapter 1 Mathematical Prerequisites 7
Linear Vector Space 7
Linear Operators 11
Self-Adjoint Operators 15
Hilbert Space and Rigged Hilbert Space 26
Probability Theory 29
Problems 38
Chapter 2 The Formulation of Quantum Mechanics 42
Basic Theoretical Concepts 42
Conditions on Operators 48
General States and Pure States 50
Probability Distributions 55
Problems 60
Chapter 3 Kinematics and Dynamics 63
Transformations of States and Observables 63
The Symmetries of Space–Time 66
Generators of the Galilei Group 68
Identification of Operators with Dynamical Variables 76
Systems 85
[[ Quantizing a Classical System ]] 87
Equations of Motion 89
Symmetries and Conservation Laws 92
Problems 94
Chapter 4 Coordinate Representation and Applications 97
Coordinate Representation 97
The Wave Equation and Its Interpretation 98
Galilei Transformation of Schr¨odinger’s Equation 102
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Probability Flux 104
Conditions on Wave Functions 106
Energy Eigenfunctions for Free Particles 109
Tunneling 110
Path Integrals 116
Problems 123
Chapter 5 Momentum Representation and Applications 126
Momentum Representation 126
Momentum Distribution in an Atom 128
Bloch’s Theorem 131
Diffraction Scattering: Theory 133
Diffraction Scattering: Experiment 139
Motion in a Uniform Force Field 145
Problems 149
Chapter 6 The Harmonic Oscillator 151
Algebraic Solution 151
Solution in Coordinate Representation 154
Solution in H Representation 157
Problems 158
Chapter 7 Angular Momentum 160
Eigenvalues and Matrix Elements 160
Explicit Form of the Angular Momentum Operators 164
Orbital Angular Momentum 166
Spin 171
Finite Rotations 175
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