Renormalized two-body low-energy scattering
Mathematical Physics
2012-03-29 v1 math.MP
Abstract
For a class of long-range potentials, including ultra-strong perturbations of the attractive Coulomb potential in dimension , we introduce a stationary scattering theory for Schr\"odinger operators which is regular at zero energy. In particular it is well defined at this energy, and we use it to establish a characterization there of the set of generalized eigenfunctions in an appropriately adapted Besov space generalizing parts of \cite{DS3}. Principal tools include global solutions to the eikonal equation and strong radiation condition bounds.
Cite
@article{arxiv.1203.6197,
title = {Renormalized two-body low-energy scattering},
author = {Erik Skibsted},
journal= {arXiv preprint arXiv:1203.6197},
year = {2012}
}