Free PDF Symplectic Geometry and Quantum Mechanics (Operator Theory: Advances and Applications)By Maurice A. de Gosson
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Symplectic Geometry and Quantum Mechanics (Operator Theory: Advances and Applications)By Maurice A. de Gosson
Free PDF Symplectic Geometry and Quantum Mechanics (Operator Theory: Advances and Applications)By Maurice A. de Gosson
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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.
- Sales Rank: #3947215 in Books
- Brand: Brand: Birkhäuser
- Published on: 2006-06-30
- Original language: English
- Number of items: 1
- Dimensions: 10.00" h x .88" w x 7.00" l, 1.97 pounds
- Binding: Hardcover
- 368 pages
- Used Book in Good Condition
Review
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)
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.
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