Extended Weyl Calculus and Application to the Phase-Space Schr\"{o}dinger Equation
De Gosson, Maurice
arXiv, 0503709 / Harvested from arXiv
Text on arXiv
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.
Publié le : 2005-03-30
Classification:  Mathematics - Symplectic Geometry,  Mathematical Physics,  MSC 81S30, 43A65, 43A32 
@article{0503709,
     author = {De Gosson, Maurice},
     title = {Extended Weyl Calculus and Application to the Phase-Space
  Schr\"{o}dinger Equation},
     journal = {arXiv},
     volume = {2005},
     number = {0},
     year = {2005},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0503709}
}

De Gosson, Maurice. Extended Weyl Calculus and Application to the Phase-Space
  Schr\"{o}dinger Equation. arXiv, Tome 2005 (2005) no. 0, . http://gdmltest.u-ga.fr/item/0503709/