Exact Time-Dependent Green's Function for the Half-Plane Barrier

Let $G$ be the time-dependent quantum mechanical propagator for a particle that is free except for a half-plane barrier with a straight edge. A closed-form exact expression for $G$ is presented in terms of the Fresnel integral for the case where the initial and final positions lie in a plane perpendicular to the edge. $G$ is not expressible as a sum over classical paths.