Abstract
We consider Schrödinger equations with variable coefficients and the harmonic potential. We suppose the perturbation is short-range type in the sense of [7]. 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 = π.
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