@article{Gosson2005,
  author    = {Gosson, Maurice A. de},
  title     = {Extended Weyl calculus and application to the phase-space Schrodinger equation},
  year      = {2005},
  abstract  = {We show that the Schrodinger 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},
  language  = {en}
}
@unpublished{Gosson2005,
  author    = {Gosson, Maurice A. de},
  title     = {Extended Weyl calculus and application to the phase-space Schr{\"o}dinger equation},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-29879},
  year      = {2005},
  abstract  = {We show that the Schr¨odinger equation in phase space proposed by Torres-Vega and Frederick is canonical in the sense that it is a natural consequence of the extendedWeyl 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.},
  language  = {en}
}
@book{Gosson2005,
  author    = {Gosson, Maurice A. de},
  title     = {Extended weyl calculus and application to the phase-space scr{\"o}dinger equation},
  series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell},
  journal   = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell},
  publisher = {Univ.},
  address   = {Potsdam},
  issn      = {1437-739X},
  pages     = {7 S.},
  year      = {2005},
  language  = {en}
}
@article{GossonGosson2006,
  author    = {Gosson, Maurice A. de and Gosson, Serge M. de},
  title     = {Extension of the Conley-Zehnder index, a product formula, and an application to the Weyl representation of metaplectic operators},
  series = {Journal of mathematical physics},
  volume    = {47},
  journal   = {Journal of mathematical physics},
  number    = {12},
  publisher = {American Institute of Physics},
  address   = {Melville},
  issn      = {0022-2488},
  doi       = {10.1063/1.239066},
  pages     = {15},
  year      = {2006},
  abstract  = {The aim of this paper is to express the Conley-Zehnder index of a symplectic path in terms of an index due to Leray and which has been studied by one of us in a previous work. This will allow us to prove a formula for the Conley-Zehnder index of the product of two symplectic paths in terms of a symplectic Cayley transform. We apply our results to a rigorous study of the Weyl representation of metaplectic operators, which plays a crucial role in the understanding of semiclassical quantization of Hamiltonian systems exhibiting chaotic behavior.},
  language  = {en}
}
@article{Gosson2005,
  author    = {Gosson, Maurice A. de},
  title     = {On the Weyl representation of metaplectic operators},
  year      = {2005},
  abstract  = {We study the Weyl representation of metaplectic operators associated to a symplectic matrix having no non- trivial fixed point, and justify a formula suggested in earlier work of Mehlig and Wilkinson. We give precise calculations of the associated Maslov-type indices; these indices intervene in a crucial way in Gutzwiller's formula of semiclassical mechanics, and are simply related to an index defined by Conley and Zehnder},
  language  = {en}
}
@unpublished{Gosson2005,
  author    = {Gosson, Maurice A. de},
  title     = {On the Weyl representation of metaplectic operators},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-29865},
  year      = {2005},
  abstract  = {We study the Weyl representation of metaplectic operators associated to a symplectic matrix having no non-trivial fixed point, and justify a formula suggested in earlier work of Mehlig and Wilkinson. We give precise calculations of the associated Maslov-type indices; these indices intervene in a crucial way in Gutzwiller's formula of semiclassical mechanics, and are simply related to an index defined by Conley and Zehnder.},
  language  = {en}
}
@book{Gosson2005,
  author    = {Gosson, Maurice A. de},
  title     = {On the weyl representation of metapletic operators},
  series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell},
  journal   = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell},
  publisher = {Univ.},
  address   = {Potsdam},
  issn      = {1437-739X},
  pages     = {15 S.},
  year      = {2005},
  language  = {en}
}
@unpublished{Gosson2006,
  author    = {Gosson, Maurice A. de},
  title     = {Symplectic geometry, Wigner-Weyl-Moyal calculus, and quantum mechanics in phase space},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-30212},
  year      = {2006},
  abstract  = {Contents: Part I: Symplectic Geometry Chapter 1: Symplectic Spaces and Lagrangian Planes Chapter 2: The Symplectic Group Chapter 3: Multi-Oriented Symplectic Geometry Chapter 4: Intersection Indices in Lag(n) and Sp(n) Part II: Heisenberg Group, Weyl Calculus, and Metaplectic Representation Chapter 5: Lagrangian Manifolds and Quantization Chapter 6: Heisenberg Group and Weyl Operators Chapter 7: The Metaplectic Group Part III: Quantum Mechanics in Phase Space Chapter 8: The Uncertainty Principle Chapter 9: The Density Operator Chapter 10: A Phase Space Weyl Calculus},
  language  = {en}
}
@book{Gosson2006,
  author    = {Gosson, Maurice A. de},
  title     = {Symplectic geometry, wigner-weyl-moyal calculus, and quantum mechanics, in phase space ; Part 1},
  series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell},
  journal   = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell},
  publisher = {Univ.},
  address   = {Potsdam},
  issn      = {1437-739X},
  pages     = {367 S.},
  year      = {2006},
  language  = {en}
}
@book{Gosson2006,
  author    = {Gosson, Maurice A. de},
  title     = {Symplectic geometry, wigner-weyl-moyal calculus, and quantum mechanics, in phase space ; Part 2},
  series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell},
  journal   = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell},
  publisher = {Univ.},
  address   = {Potsdam},
  issn      = {1437-739X},
  pages     = {367 S.},
  year      = {2006},
  language  = {en}
}