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Advances in High Energy Physics
Volume 2015 (2015), Article ID 701042, 9 pages
Research Article

Klein-Gordon Equation with Superintegrable Systems: Kepler-Coulomb, Harmonic Oscillator, and Hyperboloid

Department of Physics, Faculty of Science, Sahand University of Technology, P.O. Box 51335-1996, Tabriz, Iran

Received 27 July 2015; Revised 26 September 2015; Accepted 15 October 2015

Academic Editor: Thomas Rössler

Copyright © 2015 V. Mohammadi et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The publication of this article was funded by SCOAP3.


We study the two-dimensional Klein-Gordon equation with spin symmetry in the presence of the superintegrable potentials. On Euclidean space, the group generators of the Schrödinger-like equation with the Kepler-Coulomb potential are represented. In addition, by Levi-Civita transformation, the Schrödinger-like equation with harmonic oscillator which is dual to the Kepler-Coulomb potential and the group generators of associated system are studied. Also, we construct the quadratic algebra of the hyperboloid superintegrable system. Then, we obtain the corresponding Casimir operators and the structure functions and the relativistic energy spectra of the corresponding quasi-Hamiltonians by using the quadratic algebra approach.