Controllability of the 1D Schrodinger equation by the flatness approach

We derive in a straightforward way the exact controllability of the 1-D Schrodinger equation with a Dirichlet boundary control. We use the so-called flatness approach, which consists in parameterizing the solution and the control by the derivatives of a "flat output". This provides an explicit control input achieving the exact controllability in the energy space. As an application, we derive an explicit pair of control inputs achieving the exact steering to zero for a simply-supported beam.