Time-dependent delta-interactions for 1D Schr\"odinger Hamiltonians
Mathematical Physics
2009-04-01 v1 Analysis of PDEs
math.MP
Abstract
The non autonomous Cauchy problem for time dependent 1D point interactions is considered. The regularity assumptions for the coupling parameter are accurately analyzed and show that the general results for non autonomous linear evolution equations in Banach spaces are far from being optimal. In the mean time, this article shows an unexpected application of paraproduct techniques, initiated by J.M. Bony for nonlinear partial differential equations, to a classical linear problem.
Keywords
Cite
@article{arxiv.0903.5452,
title = {Time-dependent delta-interactions for 1D Schr\"odinger Hamiltonians},
author = {Taoufik Hmidi and Andrea Mantile and Francis Nier},
journal= {arXiv preprint arXiv:0903.5452},
year = {2009}
}