Controllability of quantum mechanical systems with continuous spectra

The property of controllability of quantum systems is revisited. In the case of a system having this property, couplings to external agents are available whose adjustment can guide the state to any chosen target on a suitably defined manifold (or arbitrarily close to any such target) at any chosen time. With due consideration to unbounded operators corresponding to physical observables possessing continuous spectra, sufficient conditions for controllability based on Lie-algebraic arguments are obtained. The results are not limited to finite-dimensional systems, nor to infinite-dimensional systems with discrete spectra. The applicability of the results to systems with both bound and scattering states is demonstrated for the case of the one-dimensional Poschl-Teller potential. Attention is also directed to transitivity of the pertinent Lie algebra of a system without drift as a necessary and sufficient condition for controllability.