Two-Dimensional Krall–Sheffer Polynomials andQuantum Systems on Spaces with Constant Curvature |
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| Authors: | Vinet Luc Zhedanov Alexei |
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| Affiliation: | (1) Department of Mathematics and Statistics and Department of Physics, McGill University, 845 Sherbrooke St. W., Montreal, QC, Canada, H3A 2T5;(2) Donetsk Institute for Physics and Technology, Donetsk, 83114, Ukraine |
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| Abstract: | Krall and Sheffer found in 1967 that there exists at most nine different types of two-dimensional orthogonal polynomials which are eigensolutions of a second-order linear differential operator with polynomial coefficients. We show that, for all these types, there correspond quantum mechanical systems on a Euclidean (pseudo-Eeuclidean) plane, two-dimensional sphere, or hyperboloid. |
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| Keywords: | integrable systems orthogonal polynomials in two variables |
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