Exact controllability in projections of the bilinear Schroedinger equation

We consider the bilinear Schrodinger equation with discrete-spectrum drift. We show, for n is an element of N arbitrary, exact controllability in projections on the first n given eigenstates. The controllability result relies on a generic controllability hypothesis on some associated finitedimensional approximations. The method is based on Lie-algebraic control techniques applied to the finite-dimensional approximations coupled with classical topological arguments issuing from degree theory.