arXiv:math/0503709 · Journal of Physics A Mathematical and General

Extended Weyl calculus and application to the phase-space Schrödinger equation

Maurice A de Gosson

Published Apr 25, 2005• 14 citations

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.

DOI: 10.1088/0305-4470/38/19/l01

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