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arXiv · hep-th/9612100

The Multidimensional Darboux Transformation

Artemio González-López·Niky Kamran
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Abstract

A generalization of the classical one-dimensional Darboux transformation to arbitrary n-dimensional oriented Riemannian manifolds is constructed using an intrinsic formulation based on the properties of twisted Hodge Laplacians. The classical two-dimensional Moutard transformation is also generalized to non-compact oriented Riemannian manifolds of dimension n greater than one. New examples of quasi-exactly solvable multidimensional matrix Schrödinger operators on curved manifolds are obtained by applying the above results.

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Artemio González-López, Niky Kamran. 1996-12-10. The Multidimensional Darboux Transformation. https://doi.org/10.1016/s0393-0440(97)00044-2

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