The Multidimensional Darboux Transformation

Details The Multidimensional Darboux Transformation The Multidimensional Darboux Transformation

1996-12-10

arxiv.org/abs/hep-th/9612100v1

J.Geom.Phys. 26 (1998) 202-226

Physics

High Energy Physics

High Energy Physics - Theory

plain TeX, 29 pages. Auxiliary file Darboux.ref and macros file ao.tex

Scientific paper

10.1016/S0393-0440(97)00044-2

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 Schr\"odinger operators on curved manifolds are obtained by applying the above results.

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