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The Multidimensional Darboux transformation González López, Artemio Kamran, Niky 51-73 Quantum-systems Supersymmetry Dimensions Física-Modelos matemáticos Física matemática © Elsevier. One of the authors (A.G.-L.) would like to thank A. Galindo, M. Mañas and M. A. Martín Delgado for helpful conversations. 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 ≥ 2. New examples of quasi-exactly solvable multidimensional matrix Schrödinger operators on curved manifolds are obtained by applying the above results. Depto. de Física Teórica Fac. de Ciencias Físicas TRUE pub 2023-06-20T20:09:56Z 2023-06-20T20:09:56Z 1998-07 journal article https://hdl.handle.net/20.500.14352/59724 0393-0440 10.1016/S0393-0440(97)00044-2 eng open access application/pdf Elsevier