Methods of modern mathematical physics: III Scattering theory

Description

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