Wave Front Set for Solutions to Perturbed Harmonic Oscillators

摘要

We consider Schrdinger 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 =