Mathematical concepts of quantum mechanics = 量子力学中的数学概念
发布日期:2011-06-30 浏览次
[内容简介]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.
[目次]1 Physical Background
2 Dynamics
3 Observables
4 The Uncertainty Principle
5 Spectral Theory
6 Scattering States
7 Special Cases
8 Many-particle Systems
9 Density Matrices
10 Perturbation Theory: Feshbach Method
11 The Eeynman Path Integral ....
12 Quasi-classical Analysis
13 Mathematical Supplement: The Calculus of Variations.
14 Resonances
15 Introduction to Quantum Field Theory
16 Quantum Electrodynamics of Non-relatlvistic Particles:The Theory of Radiation
17 Supplement: Renormalization Group
18 Comments on Missing Topics Literatnre and Further Reading
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