Gustafson S.J., Sigal I.M. Mathematical Concepts of Quantum Mechanics

Springer-Verlag Berlin, 2003, 249 pages, ISBN: 3540441603The book gives a streamlined introduction to quantum mechanics, while describing the basic mathematical structures underpinning this discipline. Starting with an overview of the key physical experiments illustrating the origin of the physical foundations, the book proceeds to a description of the basic notions of quantum mechanics and their mathematical content. It then makes its way to topics of current interest, specifically those in which mathematics plays an important role. The topics presented include spectral theory, many-body theory, positive temperatures, path integrals and quasiclassical asymptotics, the theory of resonances, an introduction to quantum field theory and the theory of radiation. The book can serve as a text for an intermediate course in quantum mechanics.Physical Background
Dynamics
Observables
The Uncertainty Principle
Spectral Theory
Scattering States
Special Cases
Many-particle Systems
Density Matrices
The Feynman Path Integral
Quasi-classical Analysis
Mathematical Supplement: the Calculus of Variations
Resonances
Introduction to Quantum Field Theory
Quantum Electrodynamics of Non-relativistic Particles: the Theory of Radiation
Supplement: Renormalization Group