2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/92379This paper provides a framework for the control of quantum mechanical systems with scattering states, i.e., systems with continuous spectra. We present the concept and prove a criterion of the approximate strong smooth controllability. Our results make non-trivial extensions from quantum systems with finite dimensional control Lie algebras to those with infinite dimensions. It also opens up many interesting problems for future studies.Quantum Physicstext