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

2005; Institute of Physics; Volume: 38; Issue: 19 Linguagem: Inglês

10.1088/0305-4470/38/19/l01

1361-6447

Maurice A. de Gosson,

Cold Atom Physics and Bose-Einstein Condensates

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.