Quantum Mechanics: Selected Topics (Selected Topics Series)

Title ......Page 3
Copyright ......Page 4
Contents ......Page 5
Preface ......Page 9
1. Introduction ......Page 11
2. States with small binding energy ......Page 18
3. Point interaction and its correspondence to boundary conditions ......Page 24
4. Particle in field of several point potentials ......Page 27
5. The Coulomb potential ......Page 30
6. Three-dimensional oscillator ......Page 38
7. Virial theorem and its generalizations ......Page 51
8. Identical particles and statistical physics ......Page 54
1. Introduction. Wave functions of continuous spectrum with l = 0 ......Page 59
2. Motion with orbital angular momentum l /= 0. Motion in the Coulomb field ......Page 67
3. Wave functions of continuous spectrum. Scattering cross-section ......Page 74
4. Optical theorem and its generalization ......Page 80
1. Analytic properties of S-matrix ......Page 85
2. \"Redundant\" poles ......Page 94
3. Properties of residues of Sl(k) ......Page 98
4. Dispersion relations ......Page 103
1. The Marchenko equation ......Page 111
2. Reflectionless potentials ......Page 116
3. Isospectral deformations of quantum oscillator ......Page 119
4. Isospectral deformations of the Schrodinger equation and invariants of the Korteweg-de Vries equation ......Page 124
1. Introduction. The Green function of the radial Schrodinger equation ......Page 133
2. Regular method of obtaining of the Green functions ......Page 138
3. Some properties of the Green functions ......Page 144
4. The Green function for several free particles ......Page 146
5. Perturbation theory. Coordinate representation ......Page 148
6. Momentum representation ......Page 153
7. The Green function in momentum representation. Operator algebra ......Page 159
8. Scattering operator ......Page 164
9. Formulae for point potentials ......Page 169
10. Perturbation theory for continious spectrum ......Page 173
11. Convergence of series of perturbation theory ......Page 178
12. The time-dependent Green function ......Page 184
1. Wave function in quasi-classical approximation ......Page 187
2. Quasi-classical approximation for the degenerate Fermi gas ......Page 192
3. Multi-dimensional case ......Page 198
4. Non-stationary problems ......Page 209
1. Introduction ......Page 223
2. Wave function of oscillator with variable frequency under action of external force ......Page 224
3. Quantum oscillator under action of external force. Transition probabilities ......Page 228
4. Parametric excitation of quantum oscillator ......Page 230
5. Oscillator with variable frequency under action of external force. Transition probabilities ......Page 237
6. Quantum oscillator and adiabatic invariants ......Page 241
7. Quasi-energy of system under action of periodic forxe ......Page 246
8. The Heisenberg representation and canonical transformations ......Page 251
1. Introduction. The Gamov theory ......Page 265
2. Wave functions ......Page 272
3. Example of quasi-stationary state ......Page 277
4. Decay of quasi-stationary state ......Page 282
5. Radioactive decay law ......Page 288
6. Generalization of normalization. Perturbation theory for quasi-stationary states ......Page 292
7. Asymptotic behaviour of wave function at r -> infty and t -> infty ......Page 295
8. Creation of unstable particle ......Page 299
9. Transition from quasi-stationary to stationary states ......Page 305
10. Collision time ......Page 308
11. Types of long-lived states ......Page 311
Appendix A. Specific cases of the Schrodinger equation spectrum ......Page 315
Appendix B. Quasi-classical properties of highly excited levels in the Coulomb field ......Page 327
Bibliography ......Page 331
Subject Index ......Page 343