  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.
