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).