Wannier functions of elliptic one-gap potentials
Soft Condensed Matter
2009-11-10 v2 Mathematical Physics
math.MP
Exactly Solvable and Integrable Systems
Abstract
Wannier functions of the one dimensional Schroedinger equation with elliptic one gap potentials are explicitly constructed. Properties of these functions are analytically and numerically investigated. In particular we derive an expression for the amplitude of the Wannier function in the origin, a power series expansion valid in the vicinity of the origin and an asymptotic expansion characterizing the decay of the Wannier function at large distances. Using these results we construct an approximate analytical expression of the Wannier function which is valid in the whole spatial domain and is in good agreement with numerical results.
Cite
@article{arxiv.cond-mat/0401440,
title = {Wannier functions of elliptic one-gap potentials},
author = {E D Belokolos and V Z Enolskii and M Salerno},
journal= {arXiv preprint arXiv:cond-mat/0401440},
year = {2009}
}
Comments
24 pages, 5 figures