Quantum particles in a moving potential

We study the behavior of a quantum particle, trapped in localized potential, when the trapping potential starts suddenly to move with constant velocity. In one dimension we have reproduced the results obtained by (Granot and Marchewka 2009 EPL 86 20007), for an attractive delta function, using an approach based on a spectral decomposition, rather than on the propagator. We have also considered the cases of Poschl-Teller and simple harmonic oscillator potentials (in one dimension) and to the hydrogen atom (in three dimensions). In this last case we have calculated explicitly the leading contribution to the ionization probability for the hydrogen atom due to a sudden movement.