現(xiàn)代數(shù)學(xué)物理方法（第3卷）

內(nèi)容概要

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.

書籍目錄

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 Levinson's 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 Green's 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　ProblemsMATERIAL 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　ProblemsList of SymbolsIndex

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