Superintegrable systems: Polynomial algebras and quasi-exactly solvable Hamiltonians

Journal Article · Sun Oct 01 04:00:00 EDT 1995 · Annals of Physics (New York)

DOI:https://doi.org/10.1006/aphy.1995.1094· OSTI ID:278890

Letourneau, P ^[1]; Vinet, L ^[2]

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1. Departement de Physique, Universite de Montreal, C.P. 6128, Succ. Centre-ville, Montreal, Quebec, Canada, H3C 3J7 (CANADA)
2. Centre de Recherches Mathematiques, Universite de Montreal, C.P. 6128, Succ. Centre-ville, Montreal, Quebec, H3C 3J7 (CANADA)

We present a study of non-relativistic superintegrable systems whose invariants are quadratic in the momenta. In two dimensions, there exist only two inequivalent classes of such systems. The symmetries responsible for the accidental degeneracies of those problems are investigated and shown to be best described in terms of polynomial algebras. We also determine the quasi-exactly solvable (QES) systems that can be obtained by dimensional reduction from the two- and three-dimensional superintegrable models, establishing in each case the equivalence between the QES Schr{umlt o}dinger equation and the spectral problem associated to a quadratic element in the questions of a Lie algebra. {copyright} 1995 Academic Press, Inc.

• OSTI ID: 278890
• Journal Information: Annals of Physics (New York), Journal Name: Annals of Physics (New York) Journal Issue: 1 Vol. 243; ISSN 0003-4916; ISSN APNYA6
• Country of Publication: United States
• Language: English

Related Subjects

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ALGEBRA
ANALYTICAL SOLUTION
ANHARMONIC OSCILLATORS
CURVILINEAR COORDINATES
QUANTUM MECHANICS
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TWO-DIMENSIONAL CALCULATIONS