Schrödinger equations on elliptic curves: symmetries, solutions and eigenvalue problem

2020/03/25 by Lychagin, Valentin, Roop, Mikhail
#34A05 #34A26 #34B09 #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2003.11260

Abstract

In this paper, we study Schrödinger equations on elliptic curves called generalized Lamé equations. We suggest a method of finding integrable potentials for Schrödinger type equations. We apply this method to the Lamé equations and provide a sequence of integrable potentials for which the eigenvalue problem is solved explicitly.

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