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

Maurice de Gosson (1)

1 Institut für Mathematik [Potsdam]

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.

Mots clés: Schrödinger equation in phase space; Weyl calculus; metaplectic

Domaines: Géométrie symplectique [math.SG]; Physique mathématique [math-ph]

Maurice de Gosson. Extended Weyl Calculus and Application to the Phase-Space Schrödinger Equation. 2005. ⟨hal-00004603⟩