TY  - INPR
A1  - Gosson, Maurice A. de
T1  - Symplectic geometry, Wigner-Weyl-Moyal calculus, and quantum mechanics in phase space
N2  - Contents: Part I: Symplectic Geometry Chapter 1: Symplectic Spaces and Lagrangian Planes Chapter 2: The Symplectic Group Chapter 3: Multi-Oriented Symplectic Geometry Chapter 4: Intersection Indices in Lag(n) and Sp(n) Part II: Heisenberg Group, Weyl Calculus, and Metaplectic Representation Chapter 5: Lagrangian Manifolds and Quantization Chapter 6: Heisenberg Group and Weyl Operators Chapter 7: The Metaplectic Group Part III: Quantum Mechanics in Phase Space Chapter 8: The Uncertainty Principle Chapter 9: The Density Operator Chapter 10: A Phase Space Weyl Calculus
T3  - Preprint - (2006) 06 
Y1  - 2006
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-30212
ER  - 
TY  - INPR
A1  - Gosson, Maurice A. de
T1  - Extended Weyl calculus and application to the phase-space Schrödinger equation
N2  - We show that the Schr¨odinger equation in phase space proposed by Torres-Vega and Frederick is canonical in the sense that it is a natural consequence of the extendedWeyl calculus obtained by letting the Heisenberg group act on functions (or half-densities) defined on phase space. This allows us, in passing, to solve rigorously the TF equation for all quadratic Hamiltonians.
T3  - Preprint - (2005) 11 
Y1  - 2005
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-29879
ER  - 
TY  - INPR
A1  - Gosson, Maurice A. de
T1  - On the Weyl representation of metaplectic operators
N2  - We study the Weyl representation of metaplectic operators associated to a symplectic matrix having no non-trivial fixed point, and justify a formula suggested in earlier work of Mehlig and Wilkinson. We give precise calculations of the associated Maslov-type indices; these indices intervene in a crucial way in Gutzwiller’s formula of semiclassical mechanics, and are simply related to an index defined by Conley and Zehnder.
T3  - Preprint - (2005) 10 
KW  - Weyl symbol
KW  - metaplectic operators
KW  - Maslov and Conley–Zehnder index
KW  - Gutzwiller formula
Y1  - 2005
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-29865
ER  -