現代數學物理方法（第4捲） 下載 mobi epub pdf 電子書 2025

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內容簡介

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.

目錄

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

前言/序言

現代數學物理方法（第4捲） 下載 mobi epub pdf txt 電子書 格式

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　在德謨剋利特的哲學中，所有原子均由同樣的實體組成，如果“實體”一詞一定要在這裏應用的話。現代物理學中的基本粒子同樣是在受限製的意義上具有質量，就同它們在受限製的意義上還具有其他的性質一樣。因為根據相對論，質量和能量本質上是相同的概念，所以我們可以說，所有基本粒子都由能量組成。把能量定義為世界的原始實體，就能解釋這一點瞭。確實，它仍包含屬於“實體”這個術語的主要性質，那就是它是守恒的。因此，前麵已經說過，現代物理學的觀點在這方麵非常接近於赫拉剋利特的觀點，如果人們把他的元素火理解為能量的話。能量事實上就是運動之物；它可以稱為一切變化的原始原因，並且能量能夠轉化為物質、熱或光。赫拉剋利特哲學中的對立麵的鬥爭能夠在不同形式的能量之間的鬥爭中發現。　

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