English

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.

Keywords

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

R2 v1 2026-06-23T14:26:30.339Z