Ionization for Three Dimensional Time-Dependent Point Interactions
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- Correggi, M., Dell’Antonio, G., Figari, R. et al. Commun. Math. Phys. (2005) 257: 169. doi:10.1007/s00220-005-1293-x
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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.