Communications in Mathematical Physics

, Volume 257, Issue 1, pp 169–192

Ionization for Three Dimensional Time-Dependent Point Interactions

  • Michele Correggi
  • Gianfausto Dell’Antonio
  • Rodolfo Figari
  • Andrea Mantile

DOI: 10.1007/s00220-005-1293-x

Cite this article as:
Correggi, M., Dell’Antonio, G., Figari, R. et al. Commun. Math. Phys. (2005) 257: 169. doi:10.1007/s00220-005-1293-x


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.

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Michele Correggi
    • 1
  • Gianfausto Dell’Antonio
    • 2
  • Rodolfo Figari
    • 3
  • Andrea Mantile
    • 4
  1. 1.International School for Advanced StudiesTriesteItaly
  2. 2.Centro Linceo InterdisciplinareRomaItaly
  3. 3.Dipartimento di Scienze FisicheUniversità di Napoli “Federico II” and Sezione INFNNapoliItaly
  4. 4.Dipartimento di Matematica e ApplicazioniUniversità di Napoli “Federico II”NapoliItaly

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