Table of Contents
Preface v
Preface to Emended Edition viii
Chapter 1 The Fundamental Concepts of Quantum Mechanics 1
1-1 Probability in quantum mechanics 2
1-2 The uncertainty principle 9
1-3 Interfering alternatives 13
1-4 Summary of probability concepts 19
1-5 Some remaining thoughts 22
1-6 The purpose of this book 23
Chapter 2 The Quantum-mechanical Law of Motion 25
2-1 The classical action 26
2-2 The quantum-mechanical amplitude 28
2-3 The classical limit 29
2-4 The sum over paths 31
2-5 Events occurring in succession 36
2-6 Some remarks 39
Chapter 3 Developing the Concepts with Special Examples 41
3-1 The free particle 42
3-2 Diffraction through a slit 47
3-3 Results for a sharp-edged slit 55
3-4 The wave function 57
3-5 Gaussian integrals 58
3-6 Motion in a potential field 62
3-7 Systems with many variables 65
3-8 Separable systems 66
3-9 The path integral as a functional 68
3-10 Interaction of a particle and a harmonic oscillator 69
3-11 Evaluation of path integrals by Fourier series 71
Chapter 4 The Schrödinger Description of Quantum Mechanics 75
4-1 The Schrödinger equation 76
4-2 The time-independent hamiltonian 84
4-3 Normalizing the free-particle wave functions 89
Chapter 5 Measurements and Operators 95
5-1 The momentum representation 96
5-2 Measurement of quantum-mechanical variables 106
5-3 Operators 112
Chapter 6 The Perturbation Method in Quantum Mechanics 119
6-1 The perturbation expansion 120
6-2 An integral equation for KV 126
6-3 An expansion for the wave function 127
6-4 The scattering of an electron by an atom 129
6-5 Time-dependent perturbations and transition amplitudes 144
Chapter 7 Transition Elements 163
7-1 Definition of the transition element 164
7-2 Functional derivatives 170
7-3 Transition elements of some special functionals 174
7-4 General results for quadratic actions 182
7-5 Transition elements and the operator notation 184
7-6 The perturbation series for a vector potential 189
7-7 The hamiltonian 192
Chapter 8 Harmonic Oscillators 197
8-1 The simple harmonic oscillator 198
8-2 The polyatomic molecule 203
8-3 Normal coordinates 208
8-4 The one-dimensional crystal 212
8-5 The approximation of continuity 218
8-6 Quantum mechanics of a line of atoms 222
8-7 The three-dimensional crystal 224
8-8 Quantum field theory 229
8-9 The forced harmonic oscillator 232
Chapter 9 Quantum Electrodynamics 235
9-1 Classical electrodynamics 237
9-2 The quantum mechanics of the rediation field 242
9-3 The ground state 244
9-4 Interaction of field and matter 247
9-5 A single electron in a radiative field 253
9-6 The Lamb shift 256
9-7 The emission of light 260
9-8 Summary 262
Chapter 10 Statistical Mechanics 267
10-1 The partition function 269
10-2 The path integral evaluation 273
10-3 Quantum-mechanical effects 279
10-4 Systems of several variables 287
10-5 Remarks on methods of derivation 296
Chapter 11 The Variational Method 299
11-1 A minimum principle 300
11-2 An application of the variational method 303
11-3 The standard variational principle 307
11-4 Slow electrons in a polar crystal 310
Chapter 12 Other Problems in Probability 321
12-1 Random pulses 322
12-2 Characteristic functions 324
12-3 Noise 327
12-4 Gaussian noise 332
12-5 Noise spectrum 334
12-6 Brownian motion 337
12-7 Quantum mechanics 341
12-8 Influence functionals 344
12-9 Influence functional from a harmonic oscillator 352
12-10 Conclusions 356
Appendix: Some Useful Definite Integrals 359
Appendix: Notes 361
Index 366
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