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\partial_{t}u =(-Δ)^{θ/2}u + V(x)u) with $0<θ<2$ via the wave packet transform (short-time Fourier transform). We clarify the relationship between the order (θ) 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.