Multidimensional integrable Schrodinger operators with matrix potential
preprintposted on 15.02.2006, 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