Lattice two-body problem with arbitrary finite range interactions
Abstract
We study the exact solution of the two-body problem on a tight-binding one-dimensional lattice, with pairwise interaction potentials which have an arbitrary but finite range. We show how to obtain the full spectrum, the bound and scattering states and the "low-energy" solutions by very efficient and easy-to-implement numerical means. All bound states are proven to be characterized by roots of a polynomial whose degree depends linearly on the range of the potential, and we discuss the connections between the number of bound states and the scattering lengths. "Low-energy" resonances can be located with great precission with the methods we introduce. Further generalizations to include more exotic interactions are also discussed.
Cite
@article{arxiv.1001.3805,
title = {Lattice two-body problem with arbitrary finite range interactions},
author = {Manuel Valiente},
journal= {arXiv preprint arXiv:1001.3805},
year = {2015}
}
Comments
6 pages, 3 figures