Continuous Maassen kernels and the inverse oscillator

  • Wilhelm von Waldenfels
Part of the Lecture Notes in Mathematics book series (LNM, volume 1626)


The quantum stochastic differential equation of the inverse oscillator in a heat bath of oscillators is solved by the means of a calculus of continuous and differentiable Maassen kernels. It is shown that the time development operator does not only map the Hilbert space of the problem into itself, but also vectors with finite moments into vectors with finite moments. The vacuum expectation of the occupancy numbers coincides for pyramidally ordered times with a classical Markovian birth process showing the avalanche character of the quantum process.


Heat Bath Rotate Wave Approximation Heisenberg Equation Real Physical System Finite Moment 
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Copyright information

© Springer-Verlag 1996

Authors and Affiliations

  • Wilhelm von Waldenfels
    • 1
  1. 1.Institut für Angewandte MathematikUniversität HeidelbergHeidelberg

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