量子力學(xué)中的數(shù)學(xué)概念

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(nèi)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(jiǎn)介

作者：(加拿大)格斯特松

書(shū)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

章節(jié)摘錄

插圖：

編輯推薦

《量子力學(xué)中的數(shù)學(xué)概念(英文版)》是由世界圖書(shū)出版公司出版。

圖書(shū)封面

圖書(shū)標(biāo)簽Tags

無(wú)

評(píng)論、評(píng)分、閱讀與下載

---

    量子力學(xué)中的數(shù)學(xué)概念 PDF格式下載

---