We study the time evolution of a three dimensional quantum particle under the action of a time-dependent point interaction fixed at the origin.We assume that the “strength” of the interaction α(t) is a periodic function with an arbitrary mean. Under very weak conditions on the Fourier coefficients of α(t), we prove that there is complete ionization as t →∞, starting from a bound state at time t = 0. Moreover we prove also that, under the same conditions, all the states of the system are scattering states.
Correggi, M., Dell'Antonio, G., Figari, R., Mantile, A. (2005). Ionization for Three Dimensional Time-Dependent Point Interactions. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 257, 169-192 [10.1007/s00220-005-1293-x].