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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...

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Bibliographic Details
Main Author: de Gosson, Maurice A.
Format: eBook
Language:English
Published: Basel Birkhäuser 2006, 2006
Edition:1st ed. 2006
Series:Advances in Partial Differential Equations
Subjects:
Quantum Physics
Mathematical Analysis
Topological Groups And Lie Groups
Lie Groups
Topological Groups
Integral Transforms And Operational Calculus
Operator Theory
Mathematical Physics
Differential Equations
Mathematical Methods In Physics
Online Access:
Collection: Springer eBooks 2005- - Collection details see MPG.ReNa
Table of Contents:
  • 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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