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Symplectic Geometry and Quantum Mechanics
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 concen...
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Autor Corporativo: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Basel :
Birkhäuser Basel : Imprint: Birkhäuser,
2006.
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| Edición: | 1st ed. 2006. |
| Colección: | Advances in Partial Differential Equations,
166 |
| Temas: | |
| Acceso en línea: | Texto Completo |
| Sumario: | 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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| Descripción Física: | XX, 368 p. online resource. |
| ISBN: | 9783764375751 |
| ISSN: | 2504-3595 ; |