Overview
- A very readable introduction to modern mathematical topics in quantum mechanics
- Solves the problem of how to teach quantum mechanics to mathematically oriented students in an optimal way
- Shows how the mathematical treatment of quantum mechanics brings insights to physics
- Useful guide to the literature
Part of the book series: Universitext (UTX)
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Table of contents (27 chapters)
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Front Matter
Keywords
About this book
The book gives a streamlined introduction to quantum mechanics while describing the basic mathematical structures underpinning this discipline.
Starting with an overview of key physical experiments illustrating the origin of the physical foundations, the book proceeds with 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 more advanced topics presented include: many-body systems, modern perturbation theory, path integrals, the theory of resonances, adiabatic theory, geometrical phases, Aharonov-Bohm effect, density functional theory, open systems, the theory of radiation (non-relativistic quantum electrodynamics), and the renormalization group.
With different selections of chapters, the book can serve as a text for an introductory, intermediate, or advanced course in quantum mechanics. Some of the sections could be used for introductions to geometrical methods in Quantum Mechanics, to quantum information theory and to quantum electrodynamics and quantum field theory.
Authors and Affiliations
About the authors
Israel Michael Sigal is the Norman Stuart Robertson chair in Applied Mathematics at the University of Toronto. He works in several areas of mathematical physics and applied mathematics.
Bibliographic Information
Book Title: Mathematical Concepts of Quantum Mechanics
Authors: Stephen J. Gustafson, Israel Michael Sigal
Series Title: Universitext
DOI: https://doi.org/10.1007/978-3-030-59562-3
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag GmbH Germany, part of Springer Nature 2020
Softcover ISBN: 978-3-030-59561-6Published: 22 October 2020
eBook ISBN: 978-3-030-59562-3Published: 21 October 2020
Series ISSN: 0172-5939
Series E-ISSN: 2191-6675
Edition Number: 3
Number of Pages: XIV, 456
Number of Illustrations: 33 b/w illustrations
Topics: Functional Analysis, Theoretical, Mathematical and Computational Physics, Quantum Physics