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|a 9783764375751
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|a de Gosson, Maurice A.
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| 245 |
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|a Symplectic Geometry and Quantum Mechanics
|h Elektronische Ressource
|c by Maurice A. de Gosson
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| 250 |
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|a 1st ed. 2006
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| 260 |
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|a Basel
|b Birkhäuser
|c 2006, 2006
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| 300 |
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|a XX, 368 p
|b online resource
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|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
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| 653 |
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|a Quantum Physics
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| 653 |
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|a Mathematical analysis
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| 653 |
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|a Topological Groups and Lie Groups
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| 653 |
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|a Lie groups
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| 653 |
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|a Topological groups
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| 653 |
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|a Integral Transforms and Operational Calculus
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| 653 |
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|a Quantum physics
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| 653 |
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|a Operator theory
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| 653 |
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|a Mathematical physics
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| 653 |
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|a Operator Theory
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| 653 |
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|a Differential Equations
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| 653 |
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|a Differential equations
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| 653 |
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|a Mathematical Methods in Physics
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| 041 |
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7 |
|a eng
|2 ISO 639-2
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| 989 |
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|b Springer
|a Springer eBooks 2005-
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| 490 |
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|a Advances in Partial Differential Equations
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| 028 |
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|a 10.1007/3-7643-7575-2
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| 856 |
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|u https://doi.org/10.1007/3-7643-7575-2?nosfx=y
|x Verlag
|3 Volltext
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| 082 |
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|a 512.482
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|a 512.55
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| 520 |
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|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
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