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Multidimensional integrable Schrodinger operators with matrix potential
preprintposted on 2006-02-15, 10:57 authored by O.A. Chalykh, V.M. Goncharenko, Alexander VeselovAlexander Veselov
The Schrodinger operators with matrix rational potential, which are D-integrable, i.e., can be intertwined with the pure Laplacian, are investigated. Corresponding potentials are uniquely determined by their singular data which are a configuration of the hyperplanes in C-n with prescribed matrices. We describe some algebraic conditions (matrix locus equations) on these data, which are sufficient for D-integrability. As the examples some matrix generalizations of the Calogero-Moser operators are considered.
- Mathematical Sciences
NotesThis is a pre-print. The definitive version: CHALYKH, O.A., GONCHARENKO, V.M., VESELOV, A.P., 1999. Multidimensional integrable Schrodinger operators with matrix potential. Journal of Mathematical Physics, 40(11), pp.5341-5355, is available at: http://jmp.aip.org/.