Ⅻ：PERTURBATION OF POINT SPECTRA

1．Finite-dimensional perturbation theory

Appendix Algebraic and geometric multiplicity of eigenvalues of finite matrices

2．Regular perturbation theory

3．Asymptotic perturbation theory

4．Summability methods in perturbation theory

5．Spectral concentration

6．Resonances and the Fermi golden rule

Notes

Problems

ⅩⅢ：SPECTRAL ANALYSIS

1．The min-max principle

2．Bound states of Schr？dinger operators Ⅰ：Quantitative methods

3．Bound states of Schr？dinger operators Ⅱ：Qualitative theory

4．Isσdisc（H）finite or infinite？

B．Bounds on N（V）in the central case

C．Bounds on N（V）in the general two-body case

4．Locating the essential spectrum Ⅰ：Weyl's theorem

5．Locating the essential spectrum Ⅲ：The HVZ theorem

6．The absence of singular continuous spectrum Ⅰ：General theory

7．The absence of singular continuous spectrum Ⅱ：Smooth perturbations

A．Weakly coupled quantum systems

B．Positive commutators and repulsive potentials

C．Local smoothness and wave operators for repulsive potentials

8．The absence of singular continuous spectrum Ⅲ：Weighted L2 spaces

9．The spectrum of tensor products

10．The absence of singular continuous spectrum Ⅳ：Dilation analytic potentials

11．Properties of eigenfunctions

12．Nondegeneracy of the ground state

Appendix 1 The Beurling-Deny criteria

Appendix 2 The Levy-Khintchine formula

13．Absence of positive eigenvalues

Appendix Unique continuation theorems for Schr？dinger operators

14．Compactness criteria and operators with compact resolvent

15．The asymptotic distribution of eigenvalues

16．Schr？dinger operators with periodic potentials

17．An introduction to the spectral theory of non-self-adjoint operators

Notes

Problems

List of Symbols

Index