Wave front set for solutions to perturbed harmonic oscillators

Details Wave front set for solutions to perturbed harmonic oscillators Wave front set for solutions to perturbed harmonic oscillators

2008-10-09

arxiv.org/abs/0810.1577v1

Mathematics

Analysis of PDEs

15 pages

Scientific paper

We consider Schr\"odinger equations with variable coefficients and the harmonic potential. We suppose the perturbation is short-range type in the sense of [Nakamura 2004]. We characterize the wave front set of the solutions to the equation in terms of the classical scattering data and the propagator of the unperturbed harmonic oscillator. In particular, we give a "recurrence of singularities" type theorem for the propagation of the period $t=\pi$.

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