Let
be a
scattering manifold, i.e., a Riemannian manifold with an asymptotically conic structure, and let
be a Schrödinger
operator on
.
One can construct a natural time-dependent scattering theory for
with
a suitable reference system, and a scattering matrix is defined accordingly. We show
here that the scattering matrices are Fourier integral operators associated to a
canonical transform on the boundary manifold generated by the geodesic flow. In
particular, we learn that the wave front sets are mapped according to the canonical
transform. These results are generalizations of a theorem by Melrose and
Zworski, but the framework and the proof are quite different. These results may
be considered as generalizations or refinements of the classical off-diagonal
smoothness of the scattering matrix for two-body quantum scattering on Euclidean
spaces.