Preface
Chapter1. Discrets Spectrm
1. Introduction
2. States with small binding energy
3. Point interaction and its correspondence to boundary conditions
4. Particle in field of several point potentials
5. The Coulomb potential
6. Three-dimensional oscillator
7. Virial theorem and its generalizations
8. Identical particles and statistical physics
Chapter2. Continuous Spectrum
1. Introduction.Wave functions of continuous spectrum withl＝0
2. Motion with orbital angular momentum l≠0 Motion in the Coulomb field
3. Wave functions of continuous spectrum.Scattering cross-section
4. Optical theorem and its generalization
Chapter 3. Analytic Properties of Wave Function
1. Analytic properties of S-matrix
2. "Redundant" poles
3. Properties of residues of St(k)
4. Dispersion relations
Chapter 4. Inverse Scattering Problem
1. The Marchenko equation
2. Reflectionless potentials
3. Isospectral deformations of quantum oscillator
4. Isospectral deformations of the Schrodinger equation and invariants of the Korteweg-de Vries equation
Chapter 5. The Green Functions and Perturbation Theory
1. Introduction. The Green function of the radial SchrSdinger equation
2. Regular method of obtaining of the Green functions
3. Some properties of the Green functions
4. The Green function for several free particles
5. Perturbation theory. Coordinate representation
6. Momentum representation
7. The Green function in momentum representation. Operator algebra
8. Scattering operator
9. Formulae for point potentials
10. Perturbation theory for continious spectrum
11. Convergence of series of perturbation theory
12. The time-dependent Green function
Chapter 6. Quasi-classical Approximation
1. Wave function in quasi-classical approximation
2. Quasi-classical approximation for the degenerate Fermi gas
3. Multi-dimensional case
4. Non-stationary problems
Chapter 7. Exact Solutions of Non-stationary Problems for Oscillator
1. Introduction
2. Wave function of oscillator with variable frequency under action of external force
3. Quantum oscillator under action of external force Transition probabilities
4. Parametric excitation of quantum oscillator
5. Oscillator with variable frequency under action of external force Transition probabilities
6. Quantum oscillator and adiabatic invariants
7. Quasi-energy of system under action of periodic force
8. The Heisenberg representation and canonical transformations
Chapter 8. Quasi-stationary States
1. Introduction. The Gamov theory
2. Wave functions
3. Example of quasi-stationary state
4. Decay of quasi-stationary state
5. Radioactive decay law
6. Generalization of normalization. Perturbation theory for quasi-stationary states
7. Asymptotic behaviour of wave function at and
8. Creation of unstable particle
9. Transition from quasi-stationary to stationary states
10. Collision time
11. Types of long-lived states
Appendix A. Specific cases of the Schrodinger equation spectrum
Appendix B. Quasi-classical properties of highly excited levels in the Coulomb field
Bibliography
Subject Index
