Superintegrable Anharmonic Oscillators on N-dimensional Curved Spaces

DOI

10.2991/jnmp.2008.15.s3.5How to use a DOI?

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 oscilla- tor 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 pre- sented. 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 superinte- grable anharmonic perturbations are explicitly constructed.

Copyright

© 2008, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - JOUR
AU  - Angel Ballesteros
AU  - Alberto Enciso
AU  - Francisco José Herranz
AU  - Orlando Ragnisco
PY  - 2008
DA  - 2008/10/01
TI  - Superintegrable Anharmonic Oscillators on N-dimensional Curved Spaces
JO  - Journal of Nonlinear Mathematical Physics
SP  - 43
EP  - 52
VL  - 15
IS  - supplement 3
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.2008.15.s3.5
DO  - 10.2991/jnmp.2008.15.s3.5
ID  - Ballesteros2008
ER  -