Extended Weyl Calculus and Application to the Phase-Space Schrödinger Equation

Details Extended Weyl Calculus and Application to the Phase-Space Schrödinger Equation Extended Weyl Calculus and Application to the Phase-Space Schrödinger Equation

2005-03-30

arxiv.org/abs/math/0503709v1

Mathematics

Symplectic Geometry

To appear in J. Phys. A: Math. and general

Scientific paper

10.1088/0305-4470/38/19/L01

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.

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