@article {2009, title = {Controllability of the discrete-spectrum Schrodinger equation driven by an external field}, journal = {Ann. Inst. H. Poincare Anal. Non Lineaire 26 (2009) 329-349}, number = {SISSA;01/2008/M}, year = {2009}, abstract = {We prove approximate controllability of the bilinear Schrodinger equation in the case in which the uncontrolled Hamiltonian has discrete nonresonant\\nspectrum. 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\\nGalerkin 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 controlled by suitable potentials.}, doi = {10.1016/j.anihpc.2008.05.001}, url = {http://hdl.handle.net/1963/2547}, author = {Thomas Chambrion and Paolo Mason and Mario Sigalotti and Ugo Boscain} }