Point interaction controls for the energy transfer in 3-D quantum systems

We consider the problem of energy-mass transfer from scattering to bound states for a one body quantum system subject to the action of a time dependent point interaction in 3-D. Under suitable assumptions on the initial state of the particle, we prove a result of local controllability of this process. Our proof exploits the finite time asymptotic analysis of fractional integral equations and the rank theorem for maps defined on Banach spaces.