Ionization for Three Dimensional Time-dependent Point Interactions

Details Ionization for Three Dimensional Time-dependent Point Interactions Ionization for Three Dimensional Time-dependent Point Interactions

2004-02-05

arxiv.org/abs/math-ph/0402011v2

Commun. Math. Phys. 257 N.1, 169-192, 2005

Physics

Mathematical Physics

Some improvements and some references added, 26 pages, LaTeX

Scientific paper

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 (\alpha(t)) is a periodic function with an arbitrary mean. Under very weak conditions on the Fourier coefficients of (\alpha(t)), we prove that there is complete ionization as (t \to \infty), 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.

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