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现代数学物理方法 第3卷PDF|Epub|txt|kindle电子书版本网盘下载

现代数学物理方法 第3卷
  • M. Reed，B. Simon 著
  • 出版社： 世界图书出版公司北京公司
  • ISBN：7506259338
  • 出版时间：2003
  • 标注页数：463页
  • 文件大小：63MB
  • 文件页数：477页
  • 主题词：

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图书目录

Ⅺ：SCATTERING THEORY1

1．An overview of scattering phenomena1

2．Classical particle scattering5

3．The basic principles of scattering in Hilbert space16

Appendix 1 Stationary phase methods37

Appendix 2 Trace ideal properties of f（x）g（-i？）47

Appendix 3 A general invariance principle for wave operators49

4．Quantum scattering Ⅰ：Two-body case54

5．Quantum scattering Ⅱ：N-body case75

6．Quantum scattering Ⅲ：Eigenfunction expansions96

Appendix Introduction to eigenfunction expansions by the auxiliary space method112

7．Quantum scattering Ⅳ：Dispersion relations116

8．Quantum scattering Ⅴ：Central potentials121

A．Reduction of the S-matrix by symmetries121

B．The partial wave expansion and its convergence127

C．Phase shifts and their connection to the Schr？dinger equation129

D．The variable phase equation133

E．Jost functions and Levinson's theorem136

F．Analyticity of the partial wave amplitude for generalized Yukawa potentials143

G．The Kohn variational principle147

Appendix 1 Legendre polynomials and spherical Bessel functions149

Appendix 2 Jost solutions for oscillatory potentials155

Appendix 3 Jost solutions and the fundamental problems of scattering theory164

9．Long-range potentials169

10．Optical and acoustical scattering Ⅰ：Schr？dinger operator184

Appendix Trace class properties of Green's functions203

11．Optical and acoustical scattering Ⅱ：The Lax-Phillips method210

Appendix The twisting trick241

12．The linear Boltzmann equation243

13．Nonlinear wave equations252

Appendix Conserved currents278

14．Spin wave scattering285

15．Quantum field scattering Ⅰ：The external field293

16．Quantum field scattering Ⅱ：The Haag-Ruelle theory317

17．Phase space analysis of scattering and spectral theory331

Appendix The RAGE theorem340

Notes344

Notes on scattering theory on C-algebras382

Problems385

MATERIAL PREPRINTED FROM VOLUME Ⅳ406

ⅩⅢ.6 The absence of singular continuous spectrum Ⅰ：General theory406

ⅩⅢ.7 The absence of singular continuous spectrum Ⅱ：Smooth perturbations411

A．Weakly coupled quantum systems421

B．Positive commutators and repulsive potentials427

C．Local smoothness and wave operators for repulsive potentials433

ⅩⅢ.8 The absence of singular continuous spectrum Ⅲ：Weighted L2 spaces438

Notes447

Problems450

List of Symbols455

Index457

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