With the publication of Volumes III and IV we have completed our presentation of the material which we originally planned as "Volume II" at the time of publication of Volume I. We originally promised the publisher that the entire series would be completed nine months after we submitted Volume I. Well! We have listed the contents of future volumes below. We are not foolhardy enough to make any predictions.

Preface

Introduction

Contents of Other Volumes

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

XlII: SPECTRAL ANALYSIS

 1. The rain-max principle

 2. Bound states of Schr‘6dinger operators I: Quantitative methods

 3. Bound states of Schr‘odinger operators II: Qualitative theory

A. Is disc (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: Tire 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 ofctensor products

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

11. Properties of eigenfitnctions

12. Nondegeneracy of the ground state

 Appendix 1 The Beurling-Deny criteria

 Appendix 2 The Levy-Khintchinecformula

13. Absence of positive eigenvalues

Appendix Unique continuation theorems for Schrodinger operators

14. Compactness criteria and operators with compact resolvent

15. The asymptotic distribution of eigenvalues

16. Schr6dinger operators with periodic potentials

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

Notes

Problems

List of Symbols

Index