Chapter 1 A review of the origins of quantum theory 1
1.1 ...and there was light! 1
1.2 The quantization of energy 5
1.3 Particle/wave duality 10
1.4 The two-slit diffraction experiment 13
1.5 Uncertainty and indeterminacy 18
1.6 Non-classical phenomena 23
References 26
Problems 27
Chapter 2 The state of a quantum system 31
2.1 The classical description of the state of a particle 31
2.2 The wave function for a single particle 33
2.3 Measurements on a quantum system 37
2.4 The wave function for a free particle 40
2.5 Free particle beams and scattering experiments 42
References 46
Problems 46
Chapter 3 The representation of dynamical variables 49
3.1 Eigenvalue equations 49
3.2 Energy eigenstates 52
3.3 Bound states of a particle in a one-dimensional square potential well 56
3.4 Scattering by a one-dimensional potential step 64
3.5 Scattering by a one-dimensional square well 68
References 74
Problems 74
Chapter 4 More about dynamical variables 79
4.1 Compatible and incompatible variables 79
4.2 The angular momentum operators 81
4.3 The radial momentum operator 84
4.4 The parity operator 86
4.5 Orbital angular momentum eigenfunctions and eigenvalues 89
4.6 Angular distributions in orbital angular momentum eigenstates 92
4.7 Rotational energy levels in nuclei and molecules 95
References 102
Problems 103
Chapter 5 Ladder operators:the one-dimensional simple harmonic oscillator 107
5.1 The energy spectrum of a one-dimensional simple harmonic oscillator 107
5.2 The energy eigenfunctions of the one-dimensional simple harmonic oscillator 111
5.3 Vibrational spectra of molecules and nuclei 115
5.4 Thermal oscillations,phonons and photons 120
References 125
Problems 126
Chapter 6 Ladder operators:angular momentum 131
6.1 The ladder operator method for the angular momentum spectrum 131
6.2 Electron spin 135
6.3 Addition of angular momenta 137
References 143
Problems 144
Chapter 7 Symmetry and the solution of the Schr？dinger equation 147
7.1 Three-dimensional systems with spherical symmetry 147
7.2 The hydrogen atom 150
7.3 Atomic structure 156
7.4 Periodic potentials and translational symmetry 160
7.5 Energy bands 165
7.6 Crystalline solids 171
References 175
Problems 176
Chapter 8 Magnetic effects in quantum systems 183
8.1 The Hamiltonian for a charged particle in an electromagnetic field 183
8.2 The effects of applied magnetic fields on atoms 187
8.3 The Stern-Gerlach experiment and electron spin 189
8.4 Spin-orbit coupling 192
8.5 The motion of free electrons in a uniform magnetic field:Landau levels 196
8.6 Periodic effects in two-dimensional conductors 199
8.7 The quantum Hall effect 202
References 206
Problems 206
Chapter 9 The superposition principle 211
9.1 The prediction of the results of experiments on quantum systems 211
9.2 The superposition expansion 213
9.3 Expectation values and uncertainties 217
9.4 Superpositions of momentum eigenfunctions 222
9.5 Position eigenstates and the Dirac delta function 227
References 229
Problems 229
Chapter 10 The matrix formulation of quantum mechanics 235
10.1 Alternatives to Schr？dinger's wave mechanics 235
10.2 The representation of the state of a particle in a discrete basis 237
10.3 The matrix representation for dynamical variables 240
10.4 Eigenvalue equations in the matrix formulation 243
10.5 A spin-half particle in a magnetic field 246
10.6 The Dirac notation 250
References 252
Problems 252
Chapter 11 Approximate methods for solving the Schr？dinger equation 255
11.1 Time-independent perturbation theory 255
11.2 First-order perturbations:a one-dimensional problem 260
11.3 Second-order perturbations:anharmonic oscillations 263
11.4 Degenerate perturbation theory:spin-orbit coupling 265
11.5 A variational method for finding the ground state of a bound particle 270
References 274
Problems 275
Chapter 12 Time-dependent problems 281
12.1 The time-dependent Schr？dinger equation 281
12.2 Resonant transitions between two energy levels 285
12.3 Time-dependent perturbation theory 289
12.4 Selection rules for electric dipole radiation spectra 293
12.5 Transition rates and Fermi's golden rule 295
12.6 High-energy elastic scattering by a finite-range potential 298
References 302
Problems 303
Chapter 13 Many-particle systems 307
13.1 The wave function for a system of non-interacting particles 307
13.2 The Born-Oppenheimer approximation 310
13.3 Identical particles and the Pauli exclusion principle 314
13.4 Systems containing two identical particles 318
References 326
Problems 326
Chapter 14 Coherence in quantum mechanics 329
14.1 Coherence in a system containing many identical particles 329
14.2 Successive Stern-Gerlach experiments 332
14.3 Two-particle correlation experiments 337
14.4 Determinism, locality and Bell's inequality 342
References 346
Problems 346
Appendix A The two-body problem in classical mechanics 349
A1 The kinetic energy of a two-particle system 349
A2 Two particles interacting through a central force 351
Appendix B Analytical solutions of eigenvalue equations 353
B1 Legendre's equation 353
B2 The energy eigenvalue equation for the simple harmonic oscillator 356
B3 The radial equation for the hydrogen atom 358
Appendix C The computer demonstrations 361
C1 The Schr？dinger equation in one dimension 362
C2 The Kronig-Penney model 365
C3 The Schr？dinger equation:central potentials 365
C4 Orbital angular momentum 366
C5 Transmission 366
C6 Wave packets 367
Index 369