Scattering theory of waves and particles
Scattering theory of waves and particles
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DOI：
10.1007/978-3-642-88128-2
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发表时间：
1966
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影响因子：
--
通讯作者：
R. Newton
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文献类型：
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作者：
R. Newton
自十五年前本书第一版出版以来，散射理论已经取得了很大进展，现在是时候更新它了。不用说，不可能将新发展的所有领域都纳入其中。由于在关于散射理论的较新书籍中，有三本优秀的书籍从更抽象的数学角度来讨论该主题（Lax 和 Phillips 关于电磁散射，Amrein、Jauch 和 Sinha，以及 Reed 和 Simon 关于量子散射），因此我没有添加有关散射理论瞬态公式的大量新数学结果的材料。唯一的例外是多拉德美丽的“散射成锥体”方法，该方法以比旧程序更令人满意的方式将物理上直观且数学上干净的波包描述与实验上可访问的散射率联系起来。大幅增强的领域包括非中心势的三维薛定谔方程的分析（第10章）、多粒子反应理论的一般方法（第16章）、三粒子散射的具体处理（第17章）和逆散射（第20章）。第 16 章的新增内容包括对二希尔伯特空间方法的介绍，以及一般散射率公式的推导。第 17 章概述了解决三粒子问题的各种方法，并对 Efimov 效应进行了讨论。
Much progress has been made in scattering theory since the publication of the first edition of this book fifteen years ago, and it is time to update it. Needless to say, it was impossible to incorporate all areas of new develop ment. Since among the newer books on scattering theory there are three excellent volumes that treat the subject from a much more abstract mathe matical point of view (Lax and Phillips on electromagnetic scattering, Amrein, Jauch and Sinha, and Reed and Simon on quantum scattering), I have refrained from adding material concerning the abundant new mathe matical results on time-dependent formulations of scattering theory. The only exception is Dollard's beautiful" scattering into cones" method that connects the physically intuitive and mathematically clean wave-packet description to experimentally accessible scattering rates in a much more satisfactory manner than the older procedure. Areas that have been substantially augmented are the analysis of the three-dimensional Schrodinger equation for non central potentials (in Chapter 10), the general approach to multiparticle reaction theory (in Chapter 16), the specific treatment of three-particle scattering (in Chapter 17), and inverse scattering (in Chapter 20). The additions to Chapter 16 include an introduction to the two-Hilbert space approach, as well as a derivation of general scattering-rate formulas. Chapter 17 now contains a survey of various approaches to the solution of three-particle problems, as well as a discussion of the Efimov effect.