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 . 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 -algebra, realized by first order differential operators.
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