In the last three decades the bilinear Schrödinger equation has been studied as a model for the evolution of finite- and infinite- dimensional closed quantum systems; some famous examples are qubits, harmonic oscillators and roto-vibrating molecules interacting with a laser. In this talk I will describe an approximate controllability test for the infinite-dimensional bilinear Schrödinger equation, based on the periodic excitation of non-degenerate modal truncations. Furthermore, I will present a recent application of this technique to study the controllability of symmetric and asymmetric rotating molecules.
