Two-dimensional Time-dependent Point Interactions
Mathematical Physics
2018-08-31 v2 math.MP
Abstract
We study the time-evolution of a quantum particle subjected to time-dependent zero-range forces in two dimensions. After establishing a conceivable ansatz for the solution to the Schr\"{o}dinger equation, we prove that the wave packet time-evolution is completely specified by the solutions of a system of Volterra-type equations -- the {\it charge equations} -- involving the coefficients of the singular part of the wave function, thus extending to the two-dimensional case known results in one and three dimensions.
Cite
@article{arxiv.1601.02390,
title = {Two-dimensional Time-dependent Point Interactions},
author = {R. Carlone and M. Correggi and R. Figari},
journal= {arXiv preprint arXiv:1601.02390},
year = {2018}
}
Comments
17 pages, AMS-LaTex; presentation of the model changed, small changes to Lemma 2.1 and Proposition 2.1