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Title: Four-dimensional singular oscillator and generalized MIC-Kepler system

Abstract

It is shown that the generalized MIC-Kepler system and four-dimensional singular oscillator are dual to each other and the duality transformation is the generalized version of the Kustaanheimo-Stiefel transformation.

Authors:
;  [1]
  1. Yerevan State University (Armenia)
Publication Date:
OSTI Identifier:
21075912
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physics of Atomic Nuclei; Journal Volume: 70; Journal Issue: 3; Other Information: DOI: 10.1134/S1063778807030180; Copyright (c) 2007 Nauka/Interperiodica; Article Copyright (c) 2007 Pleiades Publishing, Ltd; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; DUALITY; FOUR-DIMENSIONAL CALCULATIONS; OSCILLATORS; TRANSFORMATIONS

Citation Formats

Mardoyan, L. G., E-mail: mardoyan@ysu.am, and Petrosyan, M. G. Four-dimensional singular oscillator and generalized MIC-Kepler system. United States: N. p., 2007. Web. doi:10.1134/S1063778807030180.
Mardoyan, L. G., E-mail: mardoyan@ysu.am, & Petrosyan, M. G. Four-dimensional singular oscillator and generalized MIC-Kepler system. United States. doi:10.1134/S1063778807030180.
Mardoyan, L. G., E-mail: mardoyan@ysu.am, and Petrosyan, M. G. Thu . "Four-dimensional singular oscillator and generalized MIC-Kepler system". United States. doi:10.1134/S1063778807030180.
@article{osti_21075912,
title = {Four-dimensional singular oscillator and generalized MIC-Kepler system},
author = {Mardoyan, L. G., E-mail: mardoyan@ysu.am and Petrosyan, M. G.},
abstractNote = {It is shown that the generalized MIC-Kepler system and four-dimensional singular oscillator are dual to each other and the duality transformation is the generalized version of the Kustaanheimo-Stiefel transformation.},
doi = {10.1134/S1063778807030180},
journal = {Physics of Atomic Nuclei},
number = 3,
volume = 70,
place = {United States},
year = {Thu Mar 15 00:00:00 EDT 2007},
month = {Thu Mar 15 00:00:00 EDT 2007}
}
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  • The Schroedinger equation for the four-dimensional double-singular oscillator is separable in Eulerian, double-polar, and spheroidal coordinates in R{sup 4}. It is shown that the coefficients for the expansion of the double-polar basis in terms of the Eulerian basis can be expressed through the Klebsch-Gordan coefficients of the group SU(2) analytically continued to real values of their arguments. The coefficients for the expansions of the spheroidal basis in terms of the Eulerian and double-polar bases are proved to satisfy three-term recursion relations.
  • We present the quadratic algebra of the generalized MICZ-Kepler system in three-dimensional Euclidean space E{sub 3} and its dual, the four-dimensional singular oscillator, in four-dimensional Euclidean space E{sub 4}. We present their realization in terms of a deformed oscillator algebra using the Daskaloyannis construction. The structure constants are, in these cases, functions not only of the Hamiltonian but also of other integrals commuting with all generators of the quadratic algebra. We also present a new algebraic derivation of the energy spectrum of the MICZ-Kepler system on the three sphere S{sup 3} using a quadratic algebra. These results point out alsomore » that results and explicit formula for structure functions obtained for quadratic, cubic, and higher order polynomial algebras in the context of two-dimensional superintegrable systems may be applied to superintegrable systems in higher dimensions with and without monopoles.« less