Wave front set of solutions to Schr\"odinger equations with time-dependent magnetic fields
Abstract
In this paper, we determine the wave front set of solutions to the Schr\"odinger equation with time-dependent magnetic fields. We considered time-dependent and `not so small' magnetic fields through the method using the wave packet transform established by K. Kato, M. Kobayashi and S. Ito. Furthermore, we checked that the fundamental solution of the Schr\"odinger equation in a spatially decaying magnetic field has no singularities as a consequence of our result.
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