  A well known result of Jaffard states that an arbitrary region on a torus
controls, in the L2 sense, solutions of the free stationary and dynamical
Schroedinger equations. In this note we show that the same result is valid in
the presence of a smooth time-independent potential. The methods apply to
continuous potentials as well and we conjecture that the L2 control is valid
for any bounded time dependent potential.
