Exact Solvability of Superintegrable Systems

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.

14 pages, AMS LaTeX

References in corpus (1)

• Periodicity and Quasi-Periodicity for Super-Integrable Hamiltonian Systems

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