Wave front set for solutions to Schrödinger equations

We consider solutions to Schrödinger equation on Rd with variable coefficients. Let H be the Schrödinger operator and let u(t) = e −itHu0 be the solution to the Schrödinger equation with the initial condition u0 ∈ L2(Rd ).We show that the wave front set of u(t) in the nontrapping region can be characterized by the wave front set of e −itH0u0, where H0 is the free Schrödinger operator. The characterization of the wave front set is given by the wave operator for the corresponding classical mechanical scattering (or equivalently, by the asymptotics of the geodesic flow). © 2008 Elsevier Inc. All rights reserved