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