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arXiv · 0710.0843

Superintegrable anharmonic oscillators on N-dimensional curved spaces

Angel Ballesteros·Alberto Encisco·Francisco J. Herranz·Orlando Ragnisco
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Abstract

The maximal superintegrability of the intrinsic harmonic oscillator potential on N-dimensional spaces with constant curvature is revisited from the point of view of sl(2)-Poisson coalgebra symmetry. It is shown how this algebraic approach leads to a straightforward definition of a new large family of quasi-maximally superintegrable perturbations of the intrinsic oscillator on such spaces. Moreover, the generalization of this construction to those N-dimensional spaces with non-constant curvature that are endowed with sl(2)-coalgebra symmetry is presented. As the first examples of the latter class of systems, both the oscillator potential on an N-dimensional Darboux space as well as several families of its quasi-maximally superintegrable anharmonic perturbations are explicitly constructed.

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Angel Ballesteros, Alberto Encisco, Francisco J. Herranz, Orlando Ragnisco. 2007-10-03. Superintegrable anharmonic oscillators on N-dimensional curved spaces. https://doi.org/10.2991/jnmp.2008.15.s3.5

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