Author(s): Michael Reed, Barry Simon
Publisher: Academic Press
Year: 1979
Language: English
Commentary: complete
Title page
Introduction
Contents of Other Volumes
XI: SCATTERING THEORY
1. An overview of scattering phenomena
2. Classical particle scattering
3. The basic principles of scattering in Hilbert space
Appendix 1 Stationary phase methods
Appendix 2 Trace ideal properties of f(x)g(-i∇)
Appendix 3 A general invariance principle for wave operators
4. Quantum scattering I: Two-body case
5. Quantum scattering II: N-body case
6. Quantum scattering III: Eigenfunction expansions
Appendix Introduction to eigenfunction expansions by the auxiliary space method
7. Quantum scattering IV: Dispersion relations
8. Quantum scattering V: Central potentials
A. Reduction of the S-matrix by symmetries
B. The partial wave expansion and its convergence
C. Phase shifts and their connection to the Schrödinger equation
D. The variable phase equation
E. Jost functions and Lev;nson"s theorem
F. Analyticity of the partial wave amplitude for generalized Yukawa potentials
G. The Kohn variational principle
Appendix 1 Legendre polynomials and spherical Bessel functions
Appendix 2 Jost solutions for oscillatory potentials
Appendix 3 Jost solutions and the fundamental problems of scattering theory
9. Long-range potentials
10. Optical and acoustical scattering I: Schrödinger operator methods
Appendix Trace class properties of Green's functions
11. Optical and acoustical scattering II: The Lax-Phillips method
Appendix The twisting trick
12. The linear Boltzmann equation
13. Nonlinear wave equations
Appendix Conserved currents
14. Spin wave scattering
15. Quantum field scattering I: The external field
16. Quantum field scattering II: The Haag-Ruelle theory
17. Phase space analysis of scattering and spectral theory
Appendix The RAGE theorem
Notes
Notes on scattering theory on C*-algebras
Problems
MATERIAL PREPRINTED FROM VOLUME IV
XIII.6 The absence of singular continuous spectrum I: General theory
XIII.7 The absence of singular continuous spectrum II: Smooth perturbations
A. Weakly coupled quantum systems
B. Positive commutators and repulsive potentials
C. Local smoothness and wave operators for repulsive potentials
XIII.8 The absence of singular continuous spectrum III: Weighted L² spaces
Notes
Problems
List of Symbols
Index
