- 作 者：M.Reed，B.Simon
- 出 版 社：北京：世界图书出版公司北京公司
- 出版年份：2003
- ISBN：7506259346
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Ⅻ：PERTURBATION OF POINT SPECTRA 1
1．Finite-dimensional perturbation theory 1
Appendix Algebraic and geometric multiplicity of eigenvalues of finite matrices 9
2．Regular perturbation theory 10
3．Asymptotic perturbation theory 25
4．Summability methods in perturbation theory 38
5．Spectral concentration 45
6．Resonances and the Fermi golden rule 51
Notes 60
Problems 69
ⅩⅢ：SPECTRAL ANALYSIS 75
1．The min-max principle 75
2．Bound states of Schr？dinger operators Ⅰ：Quantitative methods 79
3．Bound states of Schr？dinger operators Ⅱ：Qualitative theory 86
4．Isσdisc（H）finite or infinite？ 86
B．Bounds on N（V）in the central case 90
C．Bounds on N（V）in the general two-body case 98
4．Locating the essential spectrum Ⅰ：Weyl's theorem 106
5．Locating the essential spectrum Ⅲ：The HVZ theorem 120
6．The absence of singular continuous spectrum Ⅰ：General theory 136
7．The absence of singular continuous spectrum Ⅱ：Smooth perturbations 141
A．Weakly coupled quantum systems 151
B．Positive commutators and repulsive potentials 157
C．Local smoothness and wave operators for repulsive potentials 163
8．The absence of singular continuous spectrum Ⅲ：Weighted L2 spaces 168
9．The spectrum of tensor products 177
10．The absence of singular continuous spectrum Ⅳ：Dilation analytic potentials 183
11．Properties of eigenfunctions 191
12．Nondegeneracy of the ground state 201
Appendix 1 The Beurling-Deny criteria 209
Appendix 2 The Levy-Khintchine formula 212
13．Absence of positive eigenvalues 222
Appendix Unique continuation theorems for Schr？dinger operators 239
14．Compactness criteria and operators with compact resolvent 244
15．The asymptotic distribution of eigenvalues 260
16．Schr？dinger operators with periodic potentials 279
17．An introduction to the spectral theory of non-self-adjoint operators 316
Notes 338
Problems 364
List of Symbols 387
Index 389