Symplectic Geometry and Quantum Mechanics

• Main Author: Gosson, Maurice de (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Basel : Birkhäuser Basel, 2006.
• Series: Operator Theory: Advances and Applications ; 166
• Subjects: Mathematics.; Topological groups.; Lie groups.; Integral transforms.; Operational calculus.; Operator theory.; Partial differential equations.; Physics.; Quantum physics.; Topological Groups, Lie Groups.; Mathematical Methods in Physics.; Partial Differential Equations.; Integral Transforms, Operational Calculus.; Operator Theory.; Quantum Physics.

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...

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.