Exact Solvability of Superintegrable Systems

Details Exact Solvability of Superintegrable Systems Exact Solvability of Superintegrable Systems

2000-11-23

arxiv.org/abs/hep-th/0011209v1

J.Math.Phys. 42 (2001) 4248-4257

Physics

High Energy Physics

High Energy Physics - Theory

14 pages, AMS LaTeX

Scientific paper

10.1063/1.1386927

It is shown that all four superintegrable quantum systems on the Euclidean plane possess the same underlying hidden algebra $sl(3)$. The gauge-rotated Hamiltonians, as well as their integrals of motion, once rewritten in appropriate coordinates, preserve a flag of polynomials. This flag corresponds to highest-weight finite-dimensional representations of the $sl(3)$-algebra, realized by first order differential operators.

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