Overview
- Complete theory of the Maslov index and its variants
- Discussion of the metaplectic group and the Conley-Zehnder index
- Rigorous mathematical treatment of the Schrödinger equation in phase space
- Includes supplementary material: sn.pub/extras
Part of the book series: Operator Theory: Advances and Applications (OT, volume 166)
Part of the book sub series: Advances in Partial Differential Equations (APDE)
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Table of contents (10 chapters)
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Symplectic Geometry
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Heisenberg Group, Weyl Calculus, and Metaplectic Representation
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Quantum Mechanics in Phase Space
Keywords
About this book
Reviews
From the reviews:
"De Gosson’s book is an exhaustive and clear description of almost all the more recent results obtained in connected areas of research like symplectiv geometry, the combinatorial theory of the Maslov index, the theory of the metaplectic group and so on. It fills an important niche in the literature." -Mircea Crâsmareanu, Analele Stiintifice
"This book concerns certain aspects of symplectic geometry and their application to quantum mechanics. … This book seems best suited to someone who already has a solid background in quantum theory and wants to learn more about the symplectic geometric techniques used in quantization. … the book contains useful information about various important topics." (Brian C. Hall, Mathematical Reviews, Issue 2007 e)
“This book covers … symplectic geometry and their applications in quantum mechanics with an emphasis on phase space methods. … The exposition is very detailed and complete proofs are given. … the book takes a particularly fresh point of view on some of the topics and contains a lot of useful information for readers with some background in quantum theory and an interest in the use of symplectic techniques.” (R. Steinbauer, Monatshefte für Mathematik, Vol. 155 (1), September, 2008)
Authors and Affiliations
Bibliographic Information
Book Title: Symplectic Geometry and Quantum Mechanics
Authors: Maurice Gosson
Series Title: Operator Theory: Advances and Applications
DOI: https://doi.org/10.1007/3-7643-7575-2
Publisher: Birkhäuser Basel
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Basel 2006
Hardcover ISBN: 978-3-7643-7574-4Published: 18 May 2006
eBook ISBN: 978-3-7643-7575-1Published: 06 August 2006
Series ISSN: 0255-0156
Series E-ISSN: 2296-4878
Edition Number: 1
Number of Pages: XX, 368
Topics: Topological Groups, Lie Groups, Mathematical Methods in Physics, Partial Differential Equations, Integral Transforms, Operational Calculus, Operator Theory, Quantum Physics