Control of the bilinear Schrödinger equation for fully coupling potentials
Résumé
We present a general result of approximate controllability for the bilinear Schrödinger equation (with wave function varying in the unit sphere of an infinite dimensional Hilbert space), under the hypothesis that the Schrödinger operator has discrete spectrum and that the control potential couples all eigenstates. The control method is based on a tracking procedure for the Galerkin approximations, lifted in SU(n). The method allows to estimate the L 1 norm of the control laws achieving controllability.
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