Exact solvability of superintegrable systems | Zendy

Piergiulio Tempesta | Zendy; Alexander V. Turbiner | Zendy; P. Winternitz | Zendy

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Exact solvability of superintegrable systems

Author(s) -

Piergiulio Tempesta,

Alexander V. Turbiner,

P. Winternitz

Publication year - 2001

Publication title -

journal of mathematical physics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.708

H-Index - 119

eISSN - 1089-7658

pISSN - 0022-2488

DOI - 10.1063/1.1386927

Subject(s) - flag (linear algebra) , mathematics , euclidean geometry , pure mathematics , algebra over a field , motion (physics) , plane (geometry) , order (exchange) , mathematical physics , mathematical analysis , physics , geometry , classical mechanics , finance , economics

It is shown that all four superintegrable quantum systems on the Euclideanplane possess the same underlying hidden algebra $sl(3)$. The gauge-rotatedHamiltonians, as well as their integrals of motion, once rewritten inappropriate coordinates, preserve a flag of polynomials. This flag correspondsto highest-weight finite-dimensional representations of the $sl(3)$-algebra,realized by first order differential operators.Comment: 14 pages, AMS LaTe

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