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Exact Solvability of Superintegrable Systems

High Energy Physics - Theory 2009-10-31 v1 Mathematical Physics math.MP Exactly Solvable and Integrable Systems

Abstract

It is shown that all four superintegrable quantum systems on the Euclidean plane possess the same underlying hidden algebra sl(3)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)sl(3)-algebra, realized by first order differential operators.

Keywords

Cite

@article{arxiv.hep-th/0011209,
  title  = {Exact Solvability of Superintegrable Systems},
  author = {Piergiulio Tempesta and Alexander V. Turbiner and Pavel Winternitz},
  journal= {arXiv preprint arXiv:hep-th/0011209},
  year   = {2009}
}

Comments

14 pages, AMS LaTeX

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