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.
IONIZATION FOR THREE DIMENSIONAL TIME DEPENDENT POINT INTERACTIONS / Figari, Rodolfo; M., Correggi; G., Dell'Antonio; A., Mantile. - In: COMMUNICATIONS IN MATHEMATICAL PHYSICS. - ISSN 0010-3616. - STAMPA. - 257:(2005), pp. 169-192. [10.1007/s00220-005-1293-x]
IONIZATION FOR THREE DIMENSIONAL TIME DEPENDENT POINT INTERACTIONS
FIGARI, RODOLFO;
2005
Abstract
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.| File | Dimensione | Formato | |
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