Partial Differential Equations / Optimal Control On the small-time local controllability of a quantum particle in a moving one-dimensional infinite square potential well

Abstract We consider a quantum charged particle in a one-dimensional infinite square potential well moving along a line. We control the acceleration of the potential well. The local controllability in large time of this nonlinear control system along the ground state trajectory has been proved recently. We prove that this local controllability does not hold in small time, even if the Schrodinger equation has an infinite speed of propagation. To cite this article: J.-M. Coron, C. R. Acad. Sci. Paris, Ser. I 342 (2006).

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