Extended Weyl Calculus and Application to the Phase-Space Schrödinger Equation
arXiv:math/0503709 · doi:10.1088/0305-4470/38/19/L01
Abstract
We show that the Schrödinger 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.
To appear in J. Phys. A: Math. and general