Ⅺ：SCATTERING THEORY 1
1．An overview of scattering phenomena 1
2．Classical particle scattering 5
3．The basic principles of scattering in Hilbert space 16
Appendix 1 Stationary phase methods 37
Appendix 2 Trace ideal properties of f（x）g（-i？） 47
Appendix 3 A general invariance principle for wave operators 49
4．Quantum scattering Ⅰ：Two-body case 54
5．Quantum scattering Ⅱ：N-body case 75
6．Quantum scattering Ⅲ：Eigenfunction expansions 96
Appendix Introduction to eigenfunction expansions by the auxiliary space method 112
7．Quantum scattering Ⅳ：Dispersion relations 116
8．Quantum scattering Ⅴ：Central potentials 121
A．Reduction of the S-matrix by symmetries 121
B．The partial wave expansion and its convergence 127
C．Phase shifts and their connection to the Schr？dinger equation 129
D．The variable phase equation 133
E．Jost functions and Levinson's theorem 136
F．Analyticity of the partial wave amplitude for generalized Yukawa potentials 143
G．The Kohn variational principle 147
Appendix 1 Legendre polynomials and spherical Bessel functions 149
Appendix 2 Jost solutions for oscillatory potentials 155
Appendix 3 Jost solutions and the fundamental problems of scattering theory 164
9．Long-range potentials 169
10．Optical and acoustical scattering Ⅰ：Schr？dinger operator 184
Appendix Trace class properties of Green's functions 203
11．Optical and acoustical scattering Ⅱ：The Lax-Phillips method 210
Appendix The twisting trick 241
12．The linear Boltzmann equation 243
13．Nonlinear wave equations 252
Appendix Conserved currents 278
14．Spin wave scattering 285
15．Quantum field scattering Ⅰ：The external field 293
16．Quantum field scattering Ⅱ：The Haag-Ruelle theory 317
17．Phase space analysis of scattering and spectral theory 331
Appendix The RAGE theorem 340
Notes 344
Notes on scattering theory on C-algebras 382
Problems 385
MATERIAL PREPRINTED FROM VOLUME Ⅳ 406
ⅩⅢ.6 The absence of singular continuous spectrum Ⅰ：General theory 406
ⅩⅢ.7 The absence of singular continuous spectrum Ⅱ：Smooth perturbations 411
A．Weakly coupled quantum systems 421
B．Positive commutators and repulsive potentials 427
C．Local smoothness and wave operators for repulsive potentials 433
ⅩⅢ.8 The absence of singular continuous spectrum Ⅲ：Weighted L2 spaces 438
Notes 447
Problems 450
List of Symbols 455
Index 457