Extended Weyl Calculus and Application to the Phase-Space Schr\"{o}dinger Equation
Symplectic Geometry
2009-11-11 v1 Mathematical Physics
math.MP
Abstract
We show that the Schr\"{o}dinger equation in phase space proposed by Torres-Vega and Frederick is canonical in the sense that it is a natural consequence of the extended Weyl 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.
Cite
@article{arxiv.math/0503709,
title = {Extended Weyl Calculus and Application to the Phase-Space Schr\"{o}dinger Equation},
author = {Maurice De Gosson},
journal= {arXiv preprint arXiv:math/0503709},
year = {2009}
}
Comments
To appear in J. Phys. A: Math. and general