Table of Contents

Preface vii
1 Introduction 1
2 Classical Physics 7
2.1 Newton's Laws 7
2.1.1 Discrete Mechanics 9
2.1.2 Continuum Mechanics 13
2.1.3 Some Mathematics 23
2.2 Statistical Physics 25
2.2.1 Classical Statistical Mechanics 26
2.2.2 Equipartition Theorem 29
2.3 Electrodynamics 31
2.3.1 Basic Principles 32
2.3.2 Some Applications 33
2.3.3 Maxwell's Equations 36
2.3.4 Electromagnetic Radiation 37
2.3.5 Source of Radiation 39
3 Some Contradictions 41
3.1 Specific Heat of Solids 41
3.2 Black-Body Radiation 46
3.2.1 Planck's Hypothesis 48
3.3 Specific Heat - Revisited 51
3.3.1 Einstein Model 51
3.3.2 Debye Model 51
3.4 Photoelectric Effect 52
3.4.1 Einstein's Analysis 54
3.5 Compton Scattering 55
3.6 Atomic Spectra 57
3.6.1 Rutherford Atom 58
3.6.2 Bohr Atom 59
4 Quantum Mechanics 63
4.1 Matter Waves 63
4.2 Davisson-Germer Experiment 65
4.3 Schrodinger Equation 65
4.3.1 One-Dimensional Wave Equation 66
4.3.2 Phase Velocity 68
4.3.3 Group Velocity 69
4.3.4 Interpretation 70
4.3.5 Differential Equation 71
4.3.6 More Mathematics 72
4.3.7 Continuity Equation 74
4.3.8 General Solution for Free Particle 76
4.3.9 Interpretation (Continued) 77
4.3.10 Include Forces 79
4.3.11 Boundary Conditions 80
4.3.12 Stationary States 81
4.4 Solution to Some One-Dimensional Problems 82
4.4.1 Particle in a One-Dimensional Box 82
4.4.2 Potential Barrier in One-Dimension 84
4.4.2.1 Scattering State 85
4.4.2.2 Reflection and Transmission Coefficients 87
4.4.3 Boundary Condition at a Wall 90
4.4.4 Simple Harmonic Oscillator 91
4.5 Three Dimensions 92
4.5.1 ClassicalContinuum Mechanics 93
4.5.2 Schrodinger Equation 95
4.5.3 Particle in a Three-Dimensional Box 96
4.5.4 Free Particle - Periodic Boundary Conditions 97
4.6 Comments on the Structure of Quantum Mechanics 98
4.7 Angular Momentum 99
4.8 Point Coulomb Potential 104
4.9 Spin 106
4.10 Identical Particles 109
4.10.1 Connection Between Spin and Statistics 109
4.10.2 Non-interacting, Spin-1/2 Fermions ("Fermi Gas") 109
4.10.3 Non-Interacting Bosons ("Bose Gas") 114
4.10.4 Quantum Statistics (T [not equal] 0) 114
4.10.5 Wave Functions 116
5 Atomic Physics 117
5.1 Vector Model for Addition of Angular Momenta 117
5.1.1 Larmor's Theorem 120
5.1.2 Effective Magnetic Moment 121
5.2 Zeeman Effect 122
5.3 Spin-Orbit Interaction 123
5.4 Thomas-Fermi Theory 125
5.4.1 Thomas-Fermi Equation 125
5.4.2 Binding Energy of Atom 131
5.4.3 Numerical Results 133
5.5 Periodic System of the Elements 136
5.5.1 Shielded Coulomb Potential 136
5.5.2 Hartree Approximation 137
5.5.3 Structure of the Single-Particle Levels 138
5.5.4 Chemical Properties of the Elements 141
6 Nuclear Physics 145
6.1 Baryons 145
6.2 [Beta]-decay 147
6.3 Mean Life 147
6.4 Deuteron 148
6.5 Atomic Masses 154
6.6 Light Nuclei 156
6.7 Semi-Empirical Mass Formula 157
6.7.1 Bulk Properties 158
6.7.2 Surface Energy 158
6.7.3 Coulomb Energy 159
6.7.4 Symmetry Energy 159
6.7.5 Pairing Energy 159
6.7.6 Empirical Fit 160
6.8 Electron Scattering 162
6.8.1 Single-Slit Diffraction 162
6.8.2 Electron Scattering from a Charge Distribution 164
6.8.3 Nuclear Charge Distribution 166
6.9 Nuclear Matter 166
6.10 Shell Model 168
6.10.1 A Simple Model 169
6.10.2 More Realistic Model 171
6.10.3 Spin-Orbit Interaction 173
6.10.4 Nuclear Spins and Parities 174
6.10.5 Schmidt Lines 175
6.11 [gamma]-Decay 177
7 Particle Physics 181
7.1 Forces 181
7.2 Particles 182
7.2.1 Electric Charge 182
7.3 Hadrons 182
7.3.1 Baryon Number 182
7.3.2 Strangeness 182
7.3.3 Isospin 183
7.3.4 Charm 187
7.4 Yukawa Interaction 188
7.5 Leptons 191
7.6 Antiparticles 193
7.7 Feynman Diagrams 194
7.8 S-matrix 194
7.8.1 Transition Rate 195
7.8.2 Cross Section 197
7.9 Feynman Diagrams (Continued) 198
7.10 Quantum Electrodynamics (QED) 199
7.10.1 [mu]-e Scattering 199
7.10.2 Anomalous Magnetic Moment of Electron 200
7.11 Quarks 201
7.11.1 Nuclear Domain 204
7.11.2 Some Applications 206
7.12 Quantum Chromodynamics (QCD) 208
7.13 Standard Model of Electroweak Interactions 211
8 Special Relativity 213
8.1 Michelson-Morley Experiment 213
8.2 Lorentz Transformation 217
8.3 Einstein's Theory 218
8.4 Time Dilation 221
8.5 Lorentz Contraction 222
8.6 Transverse Dimension 223
8.7 Minkowski Space 225
8.8 Four-Vectors 230
8.9 Some Applications 233
8.9.1 Relativistic Kinematics 233
8.9.2 White Dwarf Stars 239
9 Relativistic Quantum Mechanics 245
9.1 The Dirac Equation 245
9.1.1 Non-Relativistic Reduction 250
9.1.2 Electromagnetic Current 252
9.1.3 Covariant Form 252
9.1.4 Dirac Hole Theory 253
9.1.5 Electromagnetic Interactions 254
9.2 Quantum Electrodynamics (QED) 255
9.3 Weak Interactions 259
9.4 Quantum Chromodynamics (QCD) 262
10 General Relativity 265
10.1 Motion on a Two-Dimensional Surface 265
10.2 Equivalence Principle 268
10.3 Local Freely Falling Frame (LF[superscript 3]) 271
10.4 Special Relativity 272
10.5 Einstein's Theory of General Relativity 272
10.6 Schwarzschild Solution 274
10.6.1 Interpretation 274
10.6.2 Some Applications 276
10.6.3 Schwarzschild Radius 277
10.6.4 Motion of a Point Mass 279
10.7 Cosmology 281
10.7.1 Robertson-Walker Metric (k = 0) 281
10.7.2 Interpretation 283
10.7.3 Horizon 285
11 Quantum Fluids 287
11.1 Superfluid [superscript 4]He 287
11.1.1 Hartree Approximation 289
11.1.2 Velocity Field 290
11.1.3 Quantized Circulation 291
11.1.4 Gross-Pitaevskii Equation 292
11.1.5 Vortex 293
11.1.6 Superfluidity 296
11.2 Superconductivity 298
11.2.1 Experimental Properties 299
11.2.2 Some Observations 300
11.2.3 Cooper Pairs 301
11.2.4 Flux Quantization 308
12 Quantum Fields 311
12.1 String 311
12.1.1 Energy 311
12.1.2 Normal Modes 312
12.1.3 Quantization 315
12.1.4 The Quantum Field 317
12.2 Electromagnetic Field 318
12.2.1 Normal Modes 318
12.2.2 Quantization 321
12.2.3 Stimulated Emission 321
12.3 Dirac Field 322
12.3.1 Anticommutation Relations 322
12.3.2 Dirac Field 323
12.3.3 Some Applications 323
12.4 Many-Particle Systems 325
13 Problems 327 Appendix A Complex Variables-A Primer 391 Appendix B Matrices 395 Appendix C Fourier Series and Fourier Integrals 401 Appendix D Some Thermodynamics 405 Appendix E Some Statistical Mechanics 409 Appendix F Some Vector Calculus 419 Appendix G Black-Body Flux 423 Appendix H Wave Functions for Identical Particles 425 H.1 Bosons 426 H.2 Fermions 427 H.3 Some Applications 431 Appendix I Transition Rate 435 Appendix J Neutrino Mixing 443 Appendix K Units 447 K.1 Standard International (SI) 447 K.2 Heaviside-Lorentz (rationalized cgs) 448 K.3 cgs 449 Appendix L Fundamental Constants 451 L.1 Conversion Factors 452 Appendix M Some Significant Names for Theoretical Physics 453 Bibliography 455 Index 461