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商品簡介
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.全書分2章，目次如下：點譜的擾動，譜分析。書中主要介紹一般定量分析方法，重點在非相對論性量子力學的哈密頓系統，其中包括五種算子譜分析方法：基本譜、離散譜、絕對連續譜、純點譜、奇異連續譜。
讀者對象：數學及物理專業的高校師生和相關專業科研人員。
讀者對象：數學及物理專業的高校師生和相關專業科研人員。
目次
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: Weyls 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
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: Weyls 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
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