  We study a system composed of a free quantum particle trapped in a box whose
walls can change their position. We prove the global approximate
controllability of the system. That is, any initial state can be driven
arbitrarily close to any target state in the Hilbert space of the free particle
with a predetermined final position of the box. To this purpose we consider
weak solutions of the Schr\"odinger equation and use a stability theorem for
the time-dependent Schr\"odinger equation.
