@book{c4bfc9b17554444f96ba29ad80554ef9,

title = "Symplectic Geometry and Quantum Mechanics",

abstract = "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 chaptersconcentrate onLagrangian 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 treatdensity matrices. In the last chapter the Weyl pseudo-differential calculus is extended to phase space in order to derive a Schr{\"o}dinger equation in phase space whose solutions are related to those of the usual Schr{\"o}dinger equation by a wave-packet transform. The text is essentially self-contained and can be used as basis for graduate courses. Many topics areof genuine interest for pure mathematicians working in geometry and topology.",

keywords = "Heisenberg group, Lie group, Weyl calculus, phase space, quantum mechanics, symplectic geometry, partial differential equations",

author = "Gosson, {Maurice de}",

editor = "Daniel Alpay",

year = "2006",

doi = "https://doi.org/10.1007/3-7643-7575-2",

language = "English",

isbn = "3764375744",

series = "Operator Theory: Advances and Applications",

publisher = "Birkhauser",

address = "Switzerland",

}