What can we hope about output tracking of bilinear quantum systems?
We consider a non-resonant bilinear Schrodinger equation with discrete spectrum driven by a scalar control. We prove that this system can approximately track any given trajectory, up to the phase of the coordinates, with arbitrary small controls. The result is valid both for bounded and unbounded Schrodinger operators. The method used relies on ﬁnite-dimensional control techniques applied to Lie groups. We provide also an example showing that no approximate tracking of
both modulus and phase is possible, even when controls are not assumed to be essentially bounded.