Logo - springer
Slogan - springer

Birkhäuser - Birkhäuser Mathematics | Symplectic Geometry and Quantum Mechanics

Symplectic Geometry and Quantum Mechanics

de Gosson, Maurice A.

2006, XX, 368 p.

A product of Birkhäuser Basel
Available Formats:

Springer eBooks may be purchased by end-customers only and are sold without copy protection (DRM free). Instead, all eBooks include personalized watermarks. This means you can read the Springer eBooks across numerous devices such as Laptops, eReaders, and tablets.

You can pay for Springer eBooks with Visa, Mastercard, American Express or Paypal.

After the purchase you can directly download the eBook file or read it online in our Springer eBook Reader. Furthermore your eBook will be stored in your MySpringer account. So you can always re-download your eBooks.


(net) price for USA

ISBN 978-3-7643-7575-1

digitally watermarked, no DRM

Included Format: PDF

download immediately after purchase

learn more about Springer eBooks

add to marked items


Hardcover version

You can pay for Springer Books with Visa, Mastercard, American Express or Paypal.

Standard shipping is free of charge for individual customers.


(net) price for USA

ISBN 978-3-7643-7574-4

free shipping for individuals worldwide

usually dispatched within 3 to 5 business days

add to marked items

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.

Content Level » Research

Keywords » Heisenberg group - Lie group - Weyl calculus - phase space - quantum mechanics - symplectic geometry

Related subjects » Birkhäuser Mathematics - Birkhäuser Physics

Table of contents / Preface 

Popular Content within this publication 



Read this Book on Springerlink

Services for this book

New Book Alert

Get alerted on new Springer publications in the subject area of Topological Groups, Lie Groups.