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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Vinet, L., Zhedanov, A. Two-Dimensional Krall–Sheffer Polynomials andQuantum Systems on Spaces with Constant Curvature. Letters in Mathematical Physics 65, 83–94 (2003). https://doi.org/10.1023/B:MATH.0000004361.34059.55
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DOI: https://doi.org/10.1023/B:MATH.0000004361.34059.55