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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 |
|---|---|
| Autor principal: | |
| Autor Corporativo: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Basel :
Birkhäuser Basel : Imprint: Birkhäuser,
2006.
|
| Edición: | 1st ed. 2006. |
| Colección: | Advances in Partial Differential Equations,
166 |
| Temas: | |
| Acceso en línea: | Texto Completo |
MARC
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| 001 | 978-3-7643-7575-1 | ||
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| 024 | 7 | |a 10.1007/3-7643-7575-2 |2 doi | |
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| 100 | 1 | |a de Gosson, Maurice A. |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 245 | 1 | 0 | |a Symplectic Geometry and Quantum Mechanics |h [electronic resource] / |c by Maurice A. de Gosson. |
| 250 | |a 1st ed. 2006. | ||
| 264 | 1 | |a Basel : |b Birkhäuser Basel : |b Imprint: Birkhäuser, |c 2006. | |
| 300 | |a XX, 368 p. |b online resource. | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 347 | |a text file |b PDF |2 rda | ||
| 490 | 1 | |a Advances in Partial Differential Equations, |x 2504-3595 ; |v 166 | |
| 505 | 0 | |a Symplectic Geometry -- Symplectic Spaces and Lagrangian Planes -- The Symplectic Group -- Multi-Oriented Symplectic Geometry -- Intersection Indices in Lag(n) and Sp(n) -- Heisenberg Group, Weyl Calculus, and Metaplectic Representation -- Lagrangian Manifolds and Quantization -- Heisenberg Group and Weyl Operators -- The Metaplectic Group -- Quantum Mechanics in Phase Space -- The Uncertainty Principle -- The Density Operator -- A Phase Space Weyl Calculus. | |
| 520 | |a 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. | ||
| 650 | 0 | |a Topological groups. | |
| 650 | 0 | |a Lie groups. | |
| 650 | 0 | |a Mathematical physics. | |
| 650 | 0 | |a Differential equations. | |
| 650 | 0 | |a Mathematical analysis. | |
| 650 | 0 | |a Operator theory. | |
| 650 | 0 | |a Quantum physics. | |
| 650 | 1 | 4 | |a Topological Groups and Lie Groups. |
| 650 | 2 | 4 | |a Mathematical Methods in Physics. |
| 650 | 2 | 4 | |a Differential Equations. |
| 650 | 2 | 4 | |a Integral Transforms and Operational Calculus. |
| 650 | 2 | 4 | |a Operator Theory. |
| 650 | 2 | 4 | |a Quantum Physics. |
| 710 | 2 | |a SpringerLink (Online service) | |
| 773 | 0 | |t Springer Nature eBook | |
| 776 | 0 | 8 | |i Printed edition: |z 9783764391256 |
| 776 | 0 | 8 | |i Printed edition: |z 9783764375744 |
| 830 | 0 | |a Advances in Partial Differential Equations, |x 2504-3595 ; |v 166 | |
| 856 | 4 | 0 | |u https://doi.uam.elogim.com/10.1007/3-7643-7575-2 |z Texto Completo |
| 912 | |a ZDB-2-SMA | ||
| 912 | |a ZDB-2-SXMS | ||
| 950 | |a Mathematics and Statistics (SpringerNature-11649) | ||
| 950 | |a Mathematics and Statistics (R0) (SpringerNature-43713) | ||