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.

中文翻译：

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椭圆曲线上的Schrödinger方程：对称性，解和特征值问题

在本文中，我们研究椭圆曲线上的Schrödinger方程，称为广义Lamé方程。我们建议一种寻找Schrödinger型方程可积势的方法。我们将此方法应用于Lamé方程，并提供了一个可积势序列，对于该序列可明确解决特征值问题。