Diffractive Theorems for the Wave Equation with Inverse Square Potential

Abstract

We first establish the presence of a diffractive front in the fundamental solution of the wave operator with a diract delta intial condition in two dimensional euclidean space caused by the potentials perturbation on the spherical laplacian. This motivates a result which restricts the propagation of singularities for the wave operator with a more general potential to precisely these diffractive fronts higher dimensional euclidean spaces. This is proven using microlocal energy estimates.