We consider Schr\"odinger equations with variable coefficients and theharmonic potential. We suppose the perturbation is short-range type in thesense of [Nakamura 2004]. We characterize the wave front set of the solutionsto the equation in terms of the classical scattering data and the propagator ofthe unperturbed harmonic oscillator. In particular, we give a "recurrence ofsingularities" type theorem for the propagation of the period $t=\pi$.
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机译：我们考虑具有可变系数和调和势的Schr \“ odinger方程。在[Nakamura 2004]的意义上，我们假设扰动是短程类型。我们根据经典散射数据和方程描述了该方程解的波前集。特别地，对于周期$ t = \ pi $的传播，我们给出了“奇异递归”型定理。
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