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Controllability of the discrete-spectrum Schrödinger equation driven by an external field. (English) Zbl 1161.35049
Summary: We prove approximate controllability of the bilinear Schrödinger equation in the case in which the uncontrolled Hamiltonian has discrete non-resonant spectrum. The results that are obtained apply both to bounded or unbounded domains and to the case in which the control potential is bounded or unbounded. The method relies on finite-dimensional techniques applied to the Galerkin approximations and permits, in addition, to get some controllability properties for the density matrix. Two examples are presented: the harmonic oscillator and the 3D well of potential, both controlled by suitable potentials.

MSC:
35Q55 NLS equations (nonlinear Schrödinger equations)
93C20 Control/observation systems governed by partial differential equations
93B05 Controllability
93B40 Computational methods in systems theory (MSC2010)
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