Superintegrability with third order integrals of motion, cubic algebras, and supersymmetric quantum mechanics. I. Rational function potentials

Journal Article · Thu Jan 15 00:00:00 EST 2009 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.3013804· OSTI ID:21175881

Marquette, Ian ^[1]

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1. Departement de Physique et Centre de Recherche Mathematique, Universite de Montreal, C. P. 6128, Succursale Centre-Ville, Montreal, Quebec H3C 3J7 (Canada)

We consider a superintegrable Hamiltonian system in a two-dimensional space with a scalar potential that allows one quadratic and one cubic integrals of motion. We construct the most general cubic algebra and we present specific realizations. We use them to calculate the energy spectrum. All classical and quantum superintegrable potentials separable in Cartesian coordinates with a third order integral are known. The general formalism is applied to quantum reducible and irreducible rational potentials separable in Cartesian coordinates in E{sub 2}. We also discuss these potentials from the point of view of supersymmetric and PT-symmetric quantum mechanics.

• OSTI ID: 21175881
• Journal Information: Journal of Mathematical Physics, Vol. 50, Issue 1; Other Information: DOI: 10.1063/1.3013804; (c) 2009 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ALGEBRA
CARTESIAN COORDINATES
ENERGY SPECTRA
FUNCTIONS
HAMILTONIANS
INTEGRALS
MATHEMATICAL SPACE
POTENTIALS
QUANTUM MECHANICS
SCALARS
SUPERSYMMETRY
TWO-DIMENSIONAL CALCULATIONS