Extended Weyl Calculus and Application to the Phase-Space Schrödinger EquationReport as inadecuate




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1 Institut für Mathematik Potsdam

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.

Keywords : Schrödinger equation in phase space Weyl calculus metaplectic





Author: Maurice De Gosson -

Source: https://hal.archives-ouvertes.fr/



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