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arXiv · hep-th/0011209

Exact Solvability of Superintegrable Systems

Piergiulio Tempesta·Alexander V. Turbiner·Pavel Winternitz
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Abstract

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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Piergiulio Tempesta, Alexander V. Turbiner, Pavel Winternitz. 2000-11-23. Exact Solvability of Superintegrable Systems. https://doi.org/10.1063/1.1386927

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