Two families of superintegrable and isospectral potentials in two dimensions

Details Two families of superintegrable and isospectral potentials in two dimensions Two families of superintegrable and isospectral potentials in two dimensions

2002-01-22

arxiv.org/abs/quant-ph/0201099v2

JMP, 43, 2133 (2002)

Physics

Quantum Physics

22 pages, only four typos are corrected

Scientific paper

10.1063/1.1463217

As an extension of the intertwining operator idea, an algebraic method which provides a link between supersymmetric quantum mechanics and quantum (super)integrability is introduced. By realization of the method in two dimensions, two infinite families of superintegrable and isospectral stationary potentials are generated. The method makes it possible to perform Darboux transformations in such a way that, in addition to the isospectral property, they acquire the superintegrability preserving property. Symmetry generators are second and fourth order in derivatives and all potentials are isospectral with one of the Smorodinsky-Winternitz potentials. Explicit expressions of the potentials, their dynamical symmetry generators and the algebra they obey as well as their degenerate spectra and corresponding normalizable states are presented.

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