Schr\"{o}dinger equations on elliptic curves: symmetries, solutions and eigenvalue problem
Mathematical Physics
2020-03-26 v1 math.MP
Abstract
In this paper, we study Schr\"{o}dinger equations on elliptic curves called generalized Lam\'{e} equations. We suggest a method of finding integrable potentials for Schr\"{o}dinger type equations. We apply this method to the Lam\'{e} equations and provide a sequence of integrable potentials for which the eigenvalue problem is solved explicitly.
Cite
@article{arxiv.2003.11260,
title = {Schr\"{o}dinger equations on elliptic curves: symmetries, solutions and eigenvalue problem},
author = {Valentin Lychagin and Mikhail Roop},
journal= {arXiv preprint arXiv:2003.11260},
year = {2020}
}
Comments
13 pages, 4 figures