Nondegenerate superintegrable systems in n-dimensional Euclidean spaces

Journal Article · Thu Mar 15 00:00:00 EDT 2007 · Physics of Atomic Nuclei

DOI:https://doi.org/10.1134/S1063778807030143· OSTI ID:21075916

Kalnins, E G ^[1]; Miller, W ^[2]; Pogosyan, G S ^[3]

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1. University of Waikato, Department of Mathematics and Statistics (New Zealand)
2. University of Minnesota, School of Mathematics (United States)
3. Joint Institute of Nuclear Research, Laboratory of Theoretical Physics (Russian Federation)

We analyze the concept of a nondegenerate superintegrable system in n-dimensional Euclidean space. Attached to this idea is the notion that every such system affords a separation of variables in one of the various types of generic elliptical coordinates that are possible in complex Euclidean space. An analysis of how these coordinates are arrived at in terms of their expression in terms of Cartesian coordinates is presented in detail. The use of well-defined limiting processes illustrates just how all these systems can be obtained from the most general nondegenerate superintegrable system in n-dimensional Euclidean space. Two examples help with the understanding of how the general results are obtained.

• OSTI ID: 21075916
• Journal Information: Physics of Atomic Nuclei, Vol. 70, Issue 3; Other Information: DOI: 10.1134/S1063778807030143; Copyright (c) 2007 Nauka/Interperiodica; Article Copyright (c) 2007 Pleiades Publishing, Ltd; Country of input: International Atomic Energy Agency (IAEA); ISSN 1063-7788
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
CARTESIAN COORDINATES
EUCLIDEAN SPACE
MANY-DIMENSIONAL CALCULATIONS