Introduction to Quantum Mechanics

CHAPTER 1. INTRODUCTION 1
1-1 Quantum mechanics, a system of dynamics 1
1-2 Evidence of the inadequacy of classical mechanics 3
1-3 Some necessary characteristics of quantum theory 14
1-4 Summary 18
CHAPTER 2. WAVE MECHANICS 21
2-1 The wave-particle duality 21
2-2 The wave function 23
2-3 The uncertainty relation 27
2-4 Wave packets 31 2-5 Summary . 34
CHAPTER 3. SCHRODINGER\'S EQUATION 36
3-1 The equation of motion of a wave function 36
3-2 One-dimensional motion past a potential hill 40
3-3 One-dimensional motion: reflection by an infinitely wide barrier 46
3-4 One-dimensional motion in a potential well 50
3-5 Particle flux 60
3-6 Summary 62
CHAPTER 4. FOURIER TECHNIQUES AND EXPECTATION VALUES . 64
4-1 The Fourier integral 64
4-2 The Kronecker delta and the Dirac delta function 66
4-3 Eigenvalue equations 69
4-4 Expectation values 71
4-5 Summary 75
CHAPTER 5. REVIEW OF CLASSICAL MECHANICS 77
5-l Introduction 77 
5-2 Generalized coordinates and Lagrange\'s equations 77 
5-3 Hamilton\'s equations 82
5-4 Poisson brackets 85
5-5 Canonical transformations 86
5-6 Summary . 88
CHAPTER 6. OPERATOR FORMALISM 90
6-1 Postulates of quantum mechanics. 90
6-2 Algebraic methods 103
6-3 Many-particle systems 109
6-4 Summary 112
CHAPTER 7. MEASUREMENT 115
7-1 The meaning of measurement 115
7-2 Photon polarization 116
7-3 Summary 121
CHAPTER 8. THE CORRESPONDENCE PRINCIPLE 122
8-1 The relation of quantum mechanics to classical mechanics 122
8-2 The transition from quantum mechanics to classical mechanics 122
8-3 The correspondence principle and the uncertainty relation. 129
8-4 The minimum uncertainty wave function 131
8-5 The uncertainty principle and the simple harmonic oscillator . 132
8-6 Summary 134
CHAPTER 9. ANGULAR MOMENTUM 137
9-1 Orbital angular-momentum operators 137
9-2 Orbital angular-momentum wave functions 142
9-3 Angular momentum in general 148
9-4 Addition of angular momenta 149
9-5 Class T operators 1 52
9-6 Summary . 1 54
CHAPTER 10. CENTRAL FORCES 1 56
1 0-1 Qualitative behavior with an attractive potential 1 56
1 0-2 The hydrogenic atom 158
1 0-3 The three-dimensional oscillator 166
1 0-4 The free particle 170
1 0-5 Parity 172
10-6 Summary. 174
CHAPTER 1 1 . MATRIX REPRESENTATIONS 176
1 1 -1 Matrix representations of wave functions and operators 176
1 1-2 Matrix algebra . 177
1 1-3 Types of matrix representation 180
1 1-4 Infinite matrices . 184
1 1-5 Summary . 186
CHAPTER 12. SPIN ANGULAR MOMENTUM 189
12-1 Matrix representation of angular-momentum operators 189
12-2 Systems with spin one-half 194
12-3 Electron-spin precession 195
12-4 Paramagnetic resonance 199
12-5 Summary . 205
CHAPTER 13. TRANSFORMATIONS OF REPRESENTATIONS 208
13-1 Introduction . 208
13-2 A geometrical analogue-Hilbert space 210
13-3 Eigenvalue equations 212
13-4 Group properties of unitary transformations 214
13-5 Continuous matrices. 214
13-6 Canonical transformations 217
13-7 Summary . 222
CHAPTER 14. APPROXIMATION METHODS. 226
14-1 The need for approximation methods 226
14-2 Time-independent perturbation theory 226
14-3 Time-dependent perturbation theory 237
14-4 Variational techniques 242
14-5 The WKB method . 245
14-6 Summary . 253
CHAPTER 15. INTERACTION WITH A STRONG ELECTROMAGNETIC FIELD. 259
15–1 The Hamiltonian of a particle in an electromagnetic field 259
15–2 Motion of a free electron in a uniform magnetic field 260
15–3 The weak-field Zeeman effect . 265
15-4 The g-factor . 269
15–5 The strong-field Zeeman effect 270
15–6 Interaction of an atomic electron with a plane electromagnetic wave . 272
15–7 Selection rules 278
15–8 Summary . 282
CHAPTER 16. SCATTERING 285
16-1 Physical concepts 285
16-2 The Born approximation 291
16-3 Partial waves 297
16-4 Summary . 308
CHAPTER 17. IDENTICAL PARTICLES 311
17-1 The particle-exchange operator 311
17-2 The Pauli principle . 312
17-3 The spin-independent Hamiltonian 315
17-4 Effect of spin symmetry on the energy of a state 318
17-5 Valence binding in the hydrogen molecule 324
17-6 Para- and ortho-hydrogen . 327
17-7 Systems of more than two particles 329
17-8 Summary . 329
CHAPTER 18. QUANTUM-STATISTICAL MECHANICS 331
18-1 Introduction . 331
18-2 The density matrix . 332
18-3 The equation of motion of the density matrix 337
18-4 Ordered and disordered ensembles 338
18-5 Stationary ensembles 342
18-6 Systems of noninteracting particles 345
18-7 Ideal gas . 349
18-8 Summary . 354
TABLE OF ATOMIC CONSTANTS . 360
INDEX . 361