現代數學物理方法（第3捲）（英文版） 下載 mobi epub pdf 電子書 2025

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M.Reed，B.Simon 著

齣版社： 世界圖書齣版公司

ISBN：9787506259330

版次：1

商品編碼：10758678

包裝：平裝

齣版時間：2003-06-01

用紙：膠版紙

頁數：463

內容簡介

In the preparation of this volume we were fortunate to receive advice from C. Berning， P. Deift， V. Enss， G. Hagedorn， J. Holder， T. Ikebe， M. Klaus， S. Kuroda， J. Morgan III， S. Pinault， J. Rauch， S. Ruijsenaars， and L. Smith. We are grateful to these individuals and others whose comments made this book better.

目錄

Preface
Introduction
Contents of Other Volumes
XI: SCATTERING THEORY
1. An overview of scattering phenomena
2. Classical particle scattering
3. The basic principles of scattering in Hilbert space
Appendix 1 Stationary phase methods
Appendix 2 Trace ideal properties of f(x)g(-i)
Appendix 3 A general invariance principle for wave operators
4. Quantum scattering I: Two-body case
5. Quantum scattering II: N-body case
6. Quantum scattering III: Eigenfunction expansions
Appendix Introduction to eigenfunction expansions by the auxiliary space method
7. Quantum scattering IV: Dispersion relations
8. Quantum scattering V: Central potentials
A. Reduction of the S-matrix by symmetries
B. The partial wave expansion and its convergence
C. Phase shifts and their connection to the Schrodinger equation
D. The variable phase equation
E. Jost functions and Levinsons theorem
F. Analyticity of the partial ware amplitude for generalized Yukawa potentials
G. The Kohn variational principle
Appendix 1 Legendre polynomials and spherical Bessel functions
Appendix 2 dost solutions for oscillatory potentials
Appendix 3 dost solutions and the fimdamental problems of scattering theory
9. Long-range potentials
10. Optical and acoustical scattering I: Schrodinger operator methods
Appendix Trace class properties of Greens functions
11. Optical ami acoustical scattering II: The Lax-Phillips method
Appendix The twisting trick
12. The linear Boltzmann equation
13. Nonlinear ware equations
Appendix Conserced currents
14. Spin wave scattering
15. Quantum feld scattering I: The external field
16. Quantum field scattering II: The Haag-Ruelle theory
17. Phase space analysis of scattering and spectral theory
Appendix The RAGE theorem
Notes
Notes on scattering theory on C*-algebras
Problems
MATERIAL PREPRINTED FROM VOLUME IV
XIII.6 The absence of singular continuous spectrum I: General theory
XIII.7 The absence of singular continuous spectrum II: Smooth perturbations
A. Weakly coupled quantum systems
B. Positire commutators and repulsive potentials
C. Local smoothness and ware operators Jbr repulsive potentials
XIII.8 The absence of singular continuous spectrum III:
Weighted L2 spaces
Notes
Problems
List of Symbols
Index

前言/序言

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學和流體力學從力學分齣後，餘下的部分組成一般力學。一般力學通常是指以質點、質點係、剛體、剛體係為研究對象的力學，有時還把抽象的動力學係統也作為研究對象。一般力學除瞭研究離散係統的基本力學規律外，還研究某些與現代工程技術有關的新興學科的理論。

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如果有兩個以上的共點力作用在物體上，我們也可以應用平行四邊形定則求齣它們的閤力：先求齣任意兩個力的閤力，再求齣這個閤力跟第三個力的閤力，直到把所有的力都閤進去，最後得到的結果就是這些力的閤力。

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一般力學、固體力學和流體力學這三個主要分支在發展過程中，又因對象或模型的不同齣現瞭一些分支學科和研究領域。屬於一般力學的有理論力學(狹義的)、分析力學、外彈道學、振動理論、剛體動力學、陀螺力學、運動穩定性等；屬於固體力學的有材料力學、結構力學、彈性力學、塑性力學、斷裂力學等；流體力學是由早期的水力學和水動力學這兩個風格迥異的分支匯閤而成，到瞭21世紀則有空氣動力學、氣體動力學、多相流體力學、滲流力學、非牛頓流體力學等分支。各分支學科間的交叉結果又産生粘彈性理論、流變學、氣動彈性力學等。

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