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Second order superintegrable systems in conformally flat spaces. IV. The classical 3D Stäckel transform and 3D classification theory
Abstract
This article is one of a series that lays the groundwork for a structure and classification theory of second order superintegrable systems, both classical and quantum, in conformally flat spaces. In the first part of the article we study the Stäckel transform (or coupling constant metamorphosis) as an invertible mapping between classical superintegrable systems on different three-dimensional spaces. We show first that all superintegrable systems with nondegenerate potentials are multiseparable and then that each such system on any conformally flat space is Stäckel equivalent to a system on a constant curvature space. In the second part of the article we classify all the superintegrable systems that admit separation in generic coordinates. We find that there are eight families of these systems.
Type
Journal Article
Type of thesis
Series
Citation
Kalnins, E.G., Kress, J.M. & Miller, W., Jr. (2006). Second order superintegrable systems in conformally flat spaces. IV. The classical 3D Stäckel transform and 3D classification theory. Journal of Mathematical Physics, 47, 043514.
Date
2006-04
Publisher
American Institute of Physics
Degree
Supervisors
Rights
Copyright 2006 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in the Journal of Mathematical Physics and may be found at http://jmp.aip.org/jmp/top.jsp