Reconstruction of singularities for solutions of Schrödinger's equation

We determine the behavior in time of singularities of solutions to some Schrödinger equations on Rⁿ. We assume the Hamiltonians are of the form H₀+V, where {Mathematical expression}, and where V is bounded and smooth with decaying derivatives. When all ω_k=0, the kernel k(t, x, y) of exp (-itH) is smooth in x for every fixed (t, y). When all ω₁ are equal but non-zero, the initial singularity "reconstructs" at times {Mathematical expression} and positions x=(-1)^my, just as if V=0;k is otherwise regular. In the general case, the singular support is shown to be contained in the union of the hyperplanes {Mathematical expression}, when ω_jt/π=l_j for j=j₁,..., j_r.