Table of contents
About this book
This book is devoted to a rather complete discussion of techniques and topics intervening in the mathematical treatment of quantum and semi-classical mechanics. It starts with a rigorous presentation of the basics of symplectic geometry and of its multiply-oriented extension. Further chapters concentrate on Lagrangian manifolds, Weyl operators and the Wigner-Moyal transform as well as on metaplectic groups and Maslov indices. Thus the keys for the mathematical description of quantum mechanics in phase space are discussed. They are followed by a rigorous geometrical treatment of the uncertainty principle. Then Hilbert-Schmidt and trace-class operators are exposed in order to treat density matrices. In the last chapter the Weyl pseudo-differential calculus is extended to phase space in order to derive a Schrödinger equation in phase space whose solutions are related to those of the usual Schrödinger equation by a wave-packet transform.
The text is essentially self-contained and can be used as basis for graduate courses. Many topics are of genuine interest for pure mathematicians working in geometry and topology.
- DOI https://doi.org/10.1007/3-7643-7575-2
- Copyright Information Birkhäuser Verlag 2006
- Publisher Name Birkhäuser Basel
- eBook Packages Mathematics and Statistics
- Print ISBN 978-3-7643-7574-4
- Online ISBN 978-3-7643-7575-1