  In this note, we consider wave packet parametrices for Schrodinger-like
evolution equations. Under an integrability condition along the flow, we prove
that the flow is then globally well-defined and bilipschitz. Under an
additional smallness assumption, we prove that the kernel of the phase space
operator decays rapidly away from the graph of the Hamilton flow. This can be
used to prove that smoothness is preserved for finite times by the flow of the
equation.
