Klein-Gordon Equation with Superintegrable Systems: Kepler-Coulomb, Harmonic Oscillator, and Hyperboloid
We study the two-dimensional Klein-Gordon equation with spin symmetry in the presence of the superintegrable potentials. On Euclidean space, the SO(3) group generators of the Schrödinger-like equation with the Kepler-Coulomb potential are represented. In addition, by Levi-Civita transformation, the...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2015-01-01
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| Series: | Advances in High Energy Physics |
| Online Access: | http://dx.doi.org/10.1155/2015/701042 |
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| Summary: | We study the two-dimensional Klein-Gordon equation with spin symmetry in the presence of the superintegrable potentials. On Euclidean space, the SO(3) 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 SU(2) 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. |
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| ISSN: | 1687-7357 1687-7365 |