Wave front set of solutions to the fractional Schrödinger equation

In this paper, we characterize the wave front sets of solutions to fractional Schrödinger equations $i{\mathrm{\partial }}_{t}u=(-\mathrm{\Delta }{)}^{\theta \mathrm{/}2}u+V(x)u$ with $0<\theta <2$ via the wave packet transform (short-time Fourier transform). We clarify the relationship between the order $\theta$ of the fractional Laplacian and the growth rate of the potential in the problem of propagation of singularities. In particular, we present a theorem that bridges the propagation mechanisms of singularities for the Schrödinger and wave equations.