  We consider the time dependent Schrodinger equation on a complex semi-simple
Lie group. We consider initial data a bi-invariant function. We prove that if
the initial data decays fast enough, and the solution decays fast enough at one
time slice, then the solution hs to vanish identically for all time. The
hypothesis for decay we impose is shown to be optimal, uniqueness fails
otherwise. We also consider the Heisenberg roup. There we show that the
presence of closed loops that arise as the projection of geodesics to the
contact plane at the origin precludes writing down a solution operator.
