For Schrödinger equations with sub-quadratically perturbed harmonic oscillators, the wave front set at any time is characterized by high-frequency decay of the wave packet transform of the initial data along the scaled classical flow.
Gr¨ ochenig, Foundations of Time-Frequency Analysis , Birkh¨ auser, Boston, 2001
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Wave front set of solutions to Schr\"odinger equations with perturbed harmonic oscillators
For Schrödinger equations with sub-quadratically perturbed harmonic oscillators, the wave front set at any time is characterized by high-frequency decay of the wave packet transform of the initial data along the scaled classical flow.