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现代数学物理方法 第4卷PDF|Epub|txt|kindle电子书版本网盘下载
- M.Reed，B.Simon 著
- 出版社： 北京：世界图书出版公司北京公司
- ISBN：7506259346
- 出版时间：2003
- 标注页数：396页
- 文件大小：58MB
- 文件页数：410页
- 主题词：
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图书目录
Ⅻ：PERTURBATION OF POINT SPECTRA1
1．Finite-dimensional perturbation theory1
Appendix Algebraic and geometric multiplicity of eigenvalues of finite matrices9
2．Regular perturbation theory10
3．Asymptotic perturbation theory25
4．Summability methods in perturbation theory38
5．Spectral concentration45
6．Resonances and the Fermi golden rule51
Notes60
Problems69
ⅩⅢ：SPECTRAL ANALYSIS75
1．The min-max principle75
2．Bound states of Schr？dinger operators Ⅰ：Quantitative methods79
3．Bound states of Schr？dinger operators Ⅱ：Qualitative theory86
4．Isσdisc（H）finite or infinite？86
B．Bounds on N（V）in the central case90
C．Bounds on N（V）in the general two-body case98
4．Locating the essential spectrum Ⅰ：Weyl's theorem106
5．Locating the essential spectrum Ⅲ：The HVZ theorem120
6．The absence of singular continuous spectrum Ⅰ：General theory136
7．The absence of singular continuous spectrum Ⅱ：Smooth perturbations141
A．Weakly coupled quantum systems151
B．Positive commutators and repulsive potentials157
C．Local smoothness and wave operators for repulsive potentials163
8．The absence of singular continuous spectrum Ⅲ：Weighted L2 spaces168
9．The spectrum of tensor products177
10．The absence of singular continuous spectrum Ⅳ：Dilation analytic potentials183
11．Properties of eigenfunctions191
12．Nondegeneracy of the ground state201
Appendix 1 The Beurling-Deny criteria209
Appendix 2 The Levy-Khintchine formula212
13．Absence of positive eigenvalues222
Appendix Unique continuation theorems for Schr？dinger operators239
14．Compactness criteria and operators with compact resolvent244
15．The asymptotic distribution of eigenvalues260
16．Schr？dinger operators with periodic potentials279
17．An introduction to the spectral theory of non-self-adjoint operators316
Notes338
Problems364
List of Symbols387
Index389