Title: Controllability of the 1D Schrödinger equation using flatness,
Abstract: We derive in a direct way the exact controllability of the 1D free
Schrödinger equation with Dirichlet boundary control. We use the so-called
flatness approach, which consists in parametrizing the solution and the control
by the derivatives of a "flat output". This provides an explicit and very
regular control achieving the exact controllability in the energy space.