We construct Darboux transformations of arbitrary order for generalized Schrodinger-type equations, the potentials of which are second-degree polynomials in the energy. Our equations are allowed to contain first-derivative terms with arbitrary coefficients, such as they occur, for example, in position-dependent mass scenarios. Our Darboux transformations are shown to be applicable to equations from the Heun class.

中文翻译：

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势能中具有二次能量相关性的广义薛定谔方程：达布变换及其在 Heun 类中的应用

我们为广义薛定谔型方程构造任意阶的 Darboux 变换，其势是能量的二次多项式。我们的方程允许包含具有任意系数的一阶导数项，例如它们出现在依赖位置的质量场景中。我们的 Darboux 变换被证明适用于 Heun 类的方程。