The Damped Oscillator: A Locally Convex Formulation

  • Daniel A. Dubin

    Open University, Milton Keynes, UK
  • Mark A. Hennings

    Rugby School, UK


We formulate the quantum system of an oscillator driven by a quantum Wiener process, in the locally convex setting based on the rigged triple . The generalized observables are taken to be the elements of . Pulling the dynamics back to phase space by means of the inverse of Weyl quantization, we prove that the time translations semigroup is equicontinuous of class . Moreover, it is differentiable, and its generator is an extension to of the known result for bounded operators.

Cite this article

Daniel A. Dubin, Mark A. Hennings, The Damped Oscillator: A Locally Convex Formulation. Publ. Res. Inst. Math. Sci. 41 (2005), no. 1, pp. 11–36

DOI 10.2977/PRIMS/1145475403