量子力学中的数学概念

出版时间：2009-8  出版社：世界图书出版公司  作者：格斯特松  页数：286  
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前言

The first fifteen chapters of these lectures （omitting four to six chapters each year） cover a one term course taken by a mixed group of senior undergraduate and junior graduate students specializing either in mathematics or physics. Typically, the mathematics students have some background in advanced analysis, while the physics students have had introductory quantum mechanics. To satisfy such a disparate audience, we decided to select material which is interesting from the viewpoint of modern theoretical physics, and which illustrates an interplay of ideas from various fields of mathematics such as operator theory, probability, differential equations, and differential geometry. Given our time constraint, we have often pursued mathematical content at the expense of rigor. However, wherever we have sacrificed the latter, we have tried to explain whether the result is an established fact, or, mathematically speaking, a conjecture, and in the former case, how a given argument can be made rigorous. The present book retains these features.Prerequisites for this book are introductory real analysis （notions of vector space, scalar product, norm, convergence, Fourier transform） and complex analysis, the theory of Lebesgue integration, and elementary differential equations. These topics are typically covered by the third year in mathematics departments. The first and third topics are also familiar to physics undergraduates. Those unfamiliar with Lebesgue integration can think about Lebesgue integrals as if they were Riemann integrals. This said, the pace of the book is not a leisurely one and requires, at least for beginners, some amount of work.

内容概要

　　The first fifteen chapters of these lectures （omitting four to six chapters each year） cover a one term course taken by a mixed group of senior undergraduate and junior graduate students specializing either in mathematics or physics. Typically， the mathematics students have some background in advanced analysis， while the physics students have had introductory quantum mechanics. To satisfy such a disparate audience， we decided to select material which is interesting from the viewpoint of modern theoretical physics， and which illustrates an interplay of ideas from various fields of mathematics such as operator theory， probability， differential equations， and differential geometry. Given our time constraint， we have often pursued mathematical content at the expense of rigor. However， wherever we have sacrificed the latter， we have tried to explain whether the result is an established fact， or， mathematically speaking， a conjecture， and in the former case， how a given argument can be made rigorous. The present book retains these features.

作者简介

作者：(加拿大)格斯特松

书籍目录

1　Physical Background2　Dynamics3　Observables4　The Uncertainty Principle5　Spectral Theory6　Scattering States7　Special Cases8　Many-particle Systems9　Density Matrices10　Perturbation Theory: Feshbach Method11  The Feynman Path Integral12　Quasi-classical Analysis13　Mathematical Supplement: The Calculus of Variations14　Resonances15  Introduction to Quantum Field Theory16　Quantum Electrodynamics of Non-relativistic Particles:The Theory of Radiation17　Supplement: Renormalization Group18  Comments on Missing Topics, Literature, and Further ReadingReferences Index

章节摘录

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《量子力学中的数学概念(英文版)》是由世界图书出版公司出版。

用户评论 (总计7条)

•   随着量子力学在信息技术中的运用已初见成果的时代，量子力学将与牛顿力学一样被人们普遍熟悉和掌握。这是一本很好的参考书，对于理工科学生更是如此。
•   比较偏重数学概念，若是想学过量子力学后严格规范一下其中的数学知识，可以仔细读读。
•   适合物理系高年级大学生或研究生阅读。对于想提高外语水平的读者，也是不错的。
•   量子力学博大精深，得多看一些书。
•   最近对物理比较感兴趣，就买了该书，同时听物理系的量子力学（本人数学系学生），发现这本书写法与物理系通常的教材顺序一样，比较讲究物理的一些基本假设，但相比而言更加注意数学语言的一般化和标准化，而且比较讲究与数学各个分支的联系。这类书的要点是告诉你某些些数学的物理背景，这样对数学概念会有一个比较真实的理解。
•   本书数学证明有些不够严谨。
•   < , >:H×H→C冒号是什么意思？:=是什么意思？||V||>0，V旁边两个绝对值符号是什么意思？