Asymptotics in all regimes for the Schr\"odinger equation with time-independent coefficients

Abstract

Using the recent analysis of the output of the low-energy resolvent of Schr\"odinger operators on asymptotically conic manifolds (including Euclidean space) when the potential is short-range, we produce detailed asymptotic expansions for the solutions of the initial-value problem for the Schr\"odinger equation (assuming Schwartz initial data). Asymptotics are calculated in all joint large-radii large-time regimes, these corresponding to the boundary hypersurfaces of a particular compactification of spacetime.