Second order superintegrable systems in conformally flat spaces. IV. The classical 3D Staeckel transform and 3D classification theory
- Department of Mathematics and Statistics, University of Waikato, Hamilton (New Zealand)
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 Staeckel 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 Staeckel 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.
- OSTI ID:
- 20768769
- Journal Information:
- Journal of Mathematical Physics, Journal Name: Journal of Mathematical Physics Journal Issue: 4 Vol. 47; ISSN JMAPAQ; ISSN 0022-2488
- Country of Publication:
- United States
- Language:
- English
Similar Records
Second-order superintegrable systems in conformally flat spaces. V. Two- and three-dimensional quantum systems
Coupling constant metamorphosis, the Staeckel transform and superintegrability