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On the small-time local controllability of a quantum particle in a moving one-dimensional infinite square potential well. (English) Zbl 1082.93002
Summary: 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 Schrödinger equation has an infinite speed of propagation.

MSC:
93B05 Controllability
35Q40 PDEs in connection with quantum mechanics
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