Symplectic Geometry and Quantum Mechanics: 166 (Operator Theory: Advances and Applications, 166) - Hardcover

De Gosson, Maurice A.

Hardcover

ISBN 10: 3764375744 ISBN 13: 9783764375744

Publisher: Birkhäuser, 2006

Synopsis

This book offers a complete discussion of techniques and topics intervening in the mathematical treatment of quantum and semi-classical mechanics. It starts with a very readable introduction to symplectic geometry. Many topics are also of genuine interest for pure mathematicians working in geometry and topology.

About this title

From the Back Cover

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.

Edition details

• Publisher: Birkhäuser
• Publication date: 2006
• Language: English
• ISBN 10: 3764375744
• ISBN 13: 9783764375744
• Binding: Hardcover
• Number of pages: 368