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

Maurice De Gosson
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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.

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Maurice De Gosson. 2005-03-30. Extended Weyl Calculus and Application to the Phase-Space Schrödinger Equation. https://doi.org/10.1088/0305-4470/38/19/l01

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