量子力學中的數學概念
出版時間：2009-8 出版社：世界圖書出版公司 作者：格斯特松 頁數：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.
內容概要
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.
作者簡介
作者：(加拿大)格斯特松
書籍目錄
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
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《量子力學中的數學概念(英文版)》是由世界圖書出版公司出版。
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用戶評論 (總計7條)
- 隨著量子力學在信息技術中的運用已初見成果的時代，量子力學將與牛頓力學一樣被人們普遍熟悉和掌握。這是一本很好的參考書，對于理工科學生更是如此。
- 比較偏重數學概念，若是想學過量子力學后嚴格規(guī)范一下其中的數學知識，可以仔細讀讀。
- 適合物理系高年級大學生或研究生閱讀。對于想提高外語水平的讀者，也是不錯的。
- 量子力學博大精深，得多看一些書。
- 最近對物理比較感興趣，就買了該書，同時聽物理系的量子力學（本人數學系學生），發(fā)現這本書寫法與物理系通常的教材順序一樣，比較講究物理的一些基本假設，但相比而言更加注意數學語言的一般化和標準化，而且比較講究與數學各個分支的聯系。這類書的要點是告訴你某些些數學的物理背景，這樣對數學概念會有一個比較真實的理解。
- 本書數學證明有些不夠嚴謹。
- < , >:H×H→C冒號是什么意思？:=是什么意思？||V||>0，V旁邊兩個絕對值符號是什么意思？