J. Wunsch
We study the time-dependent Schrödinger equation
on 
with an
asymptotically Euclidean metric, or, more generally, on a manifold with
boundary M, equipped with a ``scattering metric.'' Microlocal smoothness
of 
turns out to be determined by growth properties of 
at 
. A sensible measure of both singularities and growth is the
``quadratic-scattering'' wavefront set, a generalization of Hörmander's
wavefront set. We prove a propagation theorem for the quadratic-scattering
wavefront set that describes singularities and growth of in
terms of singularities and growth of . This theorem generalizes a
similar result of Craig, Kappeler and Strauss.