CONTENTS
Chapter 1 THE SPECIAL THEORY OF RELATIVITY = 1
1. Classical Principle of Relativity : Galilean Transformation = 1
2. Electromagnetic Theory and the Galilean Transformation = 3
3. The Michelson-Morley Experiment = 6
4. The Postulates of Special Relativity = 8
5. The Lorentz Transformation = 9
6. Relativistic Kinematics = 10
7. Relativistic Dynamics = 15
8. Four-Vector Notation = 21
9. Relativistic Collisions = 27
10. The Creation and Annihilation of Particles = 32
11. The Relativistic Doppler Shift = 35
12. Geometric Representations = 38
Summary = 41
Suggested References = 42
Chapter 2 THE BEGINNINGS OF THE QUANTUM THEORY = 43
1. Blackbody Radiation = 43
2. The Rayleigh-Jeans Theory = 45
3. Planck's Quantum Theory of Radiation = 46
4. Einstein's Transition Probabilities = 50
5. The Particle Nature of Photons = 54
6. The Photoelectric Effect = 54
7. The Compton Effect = 57
8. The Dual Nature of the Photon = 60
9. The Heisenberg Uncertainty Principle = 62
Summary = 64
APPENDICES A to C = 65
Appendix A. Calculation of Jeans' Number = 65
Appendix B. The Maxwell-Boltzmann Distribution Function = 67
Appendix C. The Maxwell Velocity Distribution Function = 70
Suggested References = 72
Chapter 3 THE CONCEPT OF THE NUCLEAR ATOM = 73
1. The Atomic Models of Thomson and Rutherford = 73
2. Classical Scattering Cross Sections = 75
3. Scattering Cross Sections in the C and L Frames = 80
4. Bohr's Theory of Atomic Spectra = 83
5. The Franck-Hertz Experiment = 88
6. X-ray Spectra and the Bohr Theory = 89
7. Nuclear Structure and Spectroscopy = 92
8. Fundamental Forces and Exchange Particles = 99
9. Angular Momenta and Magnetic Moments = 101
10. The Larmor Theorem and the Normal Zeeman Effect = 104
11. Spatial Quantization = 107
Summary = 110
Suggested References = 110
Chapter 4 THE DEVELOPMENT OF WAVE MECHANICS = 111
1. Introduction = 111
2. The Old Quantum Theory : Wilson-Sommerfeld Quantization Rules = 112
3. Sommerfeld's Relativistic Theory of the Hydrogen Atom = 114
4. The Wave Nature of Particles = 120
5. The Diffraction of Particles = 121
6. The Wave Function for an Electron = 126
7. The Fourier Integral and the Delta Function = 130
8. Particles as Wave Packets = 135
9. The Schr o ·· dinger Wave Equation = 141
10. The Conservation of Probability Density = 143
11. Observables, Operators, and Expectation Values = 146
12. Separation of Space and Time in the Schr o ·· dinger Equation : Energy Eigenvalues = 150
13. Dirac Bracket Notation = 154
Summary = 154
APPENDIX A = 156
Appendix A. Natural Units = 156
Suggested References = 157
Chapter 5 SOLUTIONS OF SOME ONE DIMENSIONAL SYSTEMS = 158
1. Step Potentials = 158
2. The Finite Potential Barrier = 162
3. The Square Well in One Dimension = 167
4. Multiple Square Wells = 174
5. The Harmonic Oscillator : Polynomial Solution = 176
6. Methods of Generating the Hermite Polynomials = 180
7. Normalization of the Harmonic Oscillator Wave Functions = 183
8. Applications to Molecular Vibrations = 189
9. The Harmonic Oscillator : Operator Method = 191
10. Expectation Values in the Operator Formalism = 200
Suggested References = 202
Chapter 6 THE FORMAL STRUCTURE OF QUANTUM MECHANICS = 201
1. The Postulates of Quantum Mechanics = 204
2. Measurements of Compatible Observables : Commuting Operators= 212
3. Linear Vector Spaces = 215
4. The Schmidt Orthogonalization Procedure = 218
5. Linear Transformations = 220
6. Dirac Bra-ket Notation = 221
7. Matrix Representations of Linear Operators = 224
8. The Matrix Form of the Eigenvalue Problem = 230
9. Change of Basis : Unitary Transformations = 232
10. Diagonalization of Matrices = 235
11. Application of Matrix Mechanics to the Harmonic Oscillator = 240
Summary = 243
Suggested References = 244
Chapter 7 THE WAVE EQUATION IN THREE DIMENSIONS = 246
1. Rectangular Coordinates in Three Dimensions = 246
2. Spherically Symmetric Potentials = 248
3. The Angular Momentum Operators = 252
4. Eigenvalues of the Angular Momentum Operators = 257
5. The Angular Momentum Eigenfunctions = 261
6. Normalization of the Angular Momentum Eigenfunctions = 264
7. The Angular Momentum Matrices = 268
8. Hydrogenic Atoms = 272
9. Magnetic Moments of Hydrogenic Electrons = 282
10. The Parity Operator = 284
Summary = 286
APPENDIX A = 288
Suggested References = 288
Chapter 8 SPIN, ADDITION OF ANGULAR MOMENTA, AND IDENTICAL PARTICLES = 289
1. Spin in the Schr o ·· dinger Formulation = 290
2. The Spin-orbit Interaction = 293
3. The Vector Model for Combining Angular Momenta = 295
4. Additional Interactions in the One-electron Problem = 300
5. Identical Particles, Exchange, and Symmetry = 302
6. Exchange Degeneracy and Exchange Energy = 307
7. The Periodic Chart and Many-electron Atoms = 309
8. Angular Momentum Vector Coupling Schemes = 311
9. The Land e · g Factor and the Zeeman. Effect = 315
10. Eigenfunctions of Coupled Angular Momenta = 321
11. Application to Two-particle Spin Functions = 326
12. Applications to Systems of Identical Particles = 328
Summary = 331
APPENDICES A to C = 333
Appendix A. The Distribution Functions Resulting from Quantum Statistics = 333
Appendix B. Ground State Electron Configurations for the Elements = 335
Appendix C. Answers to Selected Problems = 337
Suggested References = 338
Chapter 9 APPROXIMATION METHODS AND APPLICATIONS = 339
1. Perturbation Theory for Stationary States = 339
2. Applications of the Perturbation Method to Non-degenerate States = 343
3. Interactions of a Charged Particle with Static Electric and Magnetic Fields = 349
4. Perturbation Theory tor Degenerate States = 354
5. Time-dependent Perturbation Theory = 357
6. Perturbations That Are Harmonic in Time = 359
7. Adiabatic and Sudden Perturbations = 366
8. The Variational Method = 369
9. The JWKB Semiclassical Approximation = 371
Summary = 377
Suggested References = 377
Chapter 10 ADDITIONAL APPLICATIONS = 379
1. The Ground State of the Helium Atom = 379
2. The Lowest Excited States of Helium = 383
3. The Heisenberg Exchange Interaction and Magnetism = 386
4. The Hartree Self-consistent Method for Multi-electron Atoms = 387
5. The Thomas-Fermi Statistical Model of the Atom = 388
6. The Hydrogen Molecule : The Covalent Bond = 390
7. Magnetic Susceptibility of an Atom =392
Suggested References = 395
Chapter 11 SCATTERING THEORY = 396
1. The Partial Wave Treatment of Scattering = 396
2. Scattering As a Perturbation : The Born Approximation = 402
3. The Green's Function Method for Scattering = 406
4. Scattering of Electrons by Atoms = 409
5. The Effects of Exchange Symmetry and Spin on Scattering Cross Sections = 411
Summary = 412
Suggested References = 412
EPILOGUE = 413
AUTHOR INDEX = 415
SUBJECT INDEX = 119
