  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.
