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We study a system composed of a free quantum particle trapped in a box whosewalls can change their position. We prove the global approximatecontrollability of the system. That is, any initial state can be drivenarbitrarily close to any target state in the Hilbert space of the free particlewith a predetermined final position of the box. To this purpose we considerweak solutions of the Schr\"odinger equation and use a stability theorem forthe time-dependent Schr\"odinger equation.

On global approximate controllability of a quantum particle in a box by moving walls