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Title: Second order superintegrable systems in conformally flat spaces. IV. The classical 3D Staeckel 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 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.

Authors:
; ;  [1]
  1. Department of Mathematics and Statistics, University of Waikato, Hamilton (New Zealand)
Publication Date:
OSTI Identifier:
20768769
Resource Type:
Journal Article
Journal Name:
Journal of Mathematical Physics
Additional Journal Information:
Journal Volume: 47; Journal Issue: 4; Other Information: DOI: 10.1063/1.2191789; (c) 2006 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0022-2488
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CLASSIFICATION; COORDINATES; COUPLING CONSTANTS; INTEGRAL EQUATIONS; MAPPING; MATHEMATICAL OPERATORS; MATHEMATICAL SPACE; POTENTIALS; SCHROEDINGER EQUATION; THREE-DIMENSIONAL CALCULATIONS; TRANSFORMATIONS

Citation Formats

Kalnins, E G, Kress, J M, Miller, W Jr, School of Mathematics, The University of New South Wales, Sydney NSW 2052, and School of Mathematics, University of Minnesota, Minneapolis, MN 55455. Second order superintegrable systems in conformally flat spaces. IV. The classical 3D Staeckel transform and 3D classification theory. United States: N. p., 2006. Web. doi:10.1063/1.2191789.
Kalnins, E G, Kress, J M, Miller, W Jr, School of Mathematics, The University of New South Wales, Sydney NSW 2052, & School of Mathematics, University of Minnesota, Minneapolis, MN 55455. Second order superintegrable systems in conformally flat spaces. IV. The classical 3D Staeckel transform and 3D classification theory. United States. https://doi.org/10.1063/1.2191789
Kalnins, E G, Kress, J M, Miller, W Jr, School of Mathematics, The University of New South Wales, Sydney NSW 2052, and School of Mathematics, University of Minnesota, Minneapolis, MN 55455. 2006. "Second order superintegrable systems in conformally flat spaces. IV. The classical 3D Staeckel transform and 3D classification theory". United States. https://doi.org/10.1063/1.2191789.
@article{osti_20768769,
title = {Second order superintegrable systems in conformally flat spaces. IV. The classical 3D Staeckel transform and 3D classification theory},
author = {Kalnins, E G and Kress, J M and Miller, W Jr and School of Mathematics, The University of New South Wales, Sydney NSW 2052 and School of Mathematics, University of Minnesota, Minneapolis, MN 55455},
abstractNote = {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.},
doi = {10.1063/1.2191789},
url = {https://www.osti.gov/biblio/20768769}, journal = {Journal of Mathematical Physics},
issn = {0022-2488},
number = 4,
volume = 47,
place = {United States},
year = {Sat Apr 15 00:00:00 EDT 2006},
month = {Sat Apr 15 00:00:00 EDT 2006}
}