現代數學物理方法(第3卷)（簡體書）

In the preparation of this volume we were fortunate to receive advice from C. Berning, P. Deift, V. Enss, G. Hagedorn, J. Holder, T. Ikebe, M. Klaus, S. Kuroda, J. Morgan III, S. Pinault, J. Rauch, S. Ruijsenaars, and L. Smith. We are grateful to these individuals and others whose comments made this book better.本卷只有一章，即散射理論，內容包括希爾伯特空間的散射，基本散射原理，量子散射，光散射，聲散射，玻耳茲曼線性方程，非線性方程，自旋波散射，量子場散射等。
讀者對象：數學及物理專業的高校師生和相關專業科研人員。
1111111111111111111111111111111111111

Preface
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 Schrodinger equation
D. The variable phase equation
E. Jost functions and Levinsons theorem
F. Analyticity of the partial ware amplitude for generalized Yukawa potentials
G. The Kohn variational principle
Appendix 1 Legendre polynomials and spherical Bessel functions
Appendix 2 dost solutions for oscillatory potentials
Appendix 3 dost solutions and the fimdamental problems of scattering theory
　9. Long-range potentials
　10. Optical and acoustical scattering I: Schrodinger operator methods
Appendix Trace class properties of Greens functions
　11. Optical ami acoustical scattering II: The Lax-Phillips method
Appendix The twisting trick
　12. The linear Boltzmann equation
　13. Nonlinear ware equations
Appendix Conserced currents
　14. Spin wave scattering
　15. Quantum feld 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. Positire commutators and repulsive potentials
C. Local smoothness and ware operators Jbr repulsive potentials
　XIII.8 The absence of singular continuous spectrum III:
Weighted L2 spaces
　Notes
　Problems
List of Symbols
Index