Coupling constant metamorphosis, the Staeckel transform and superintegrability
- Centre de Recherches Mathematiques, C.P. 6128 succ. Centre-Ville, Montreal (QC) H3C 3J7 (Canada)
This paper is dedicated to the memory of Marcos Moshinsky. In this paper, we discuss the important role that coupling constant metamorphosis (CCM) and the Staeckel transform have played in the analysis of superintegrable systems. We explain the relation between the two and in particular show that they coincide when transforming between second-order superintegrable systems. Unlike in the case of second-order superintegrability, the quantum analog of CCM has only been proven for a subclass of systems with integrals of a specific form. We give the proof and as an application show the mapping of a family of superintegrable deformations of the simple harmonic oscillator to an associated family of superintegrable deformations of the Kepler-Coulomb potential.
- OSTI ID:
- 21511340
- Journal Information:
- AIP Conference Proceedings, Vol. 1323, Issue 1; Conference: Symposium on symmetries in nature in memoriam Marcos Moshinsky, Cuernavaca (Mexico), 7-14 Aug 2010; Other Information: DOI: 10.1063/1.3537855; (c) 2010 American Institute of Physics; ISSN 0094-243X
- Country of Publication:
- United States
- Language:
- English
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