Harmonic Oscillator on the SO(2,2) Hyperboloid
In the present work the classical problem of harmonic oscillator in the hyperbolic space H²₂: z²₀+z²₁−z²₂−z²₃=R² has been completely solved in framework of Hamilton-Jacobi equation. We have shown that the harmonic oscillator on H²₂, as in the other spaces with constant curvature, is exactly solvable...
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| Datum: | 2015 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | English |
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Інститут математики НАН України
2015
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| Schriftenreihe: | Symmetry, Integrability and Geometry: Methods and Applications |
| Online Zugang: | http://dspace.nbuv.gov.ua/handle/123456789/147158 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Harmonic Oscillator on the SO(2,2) Hyperboloid / D.R. Petrosyan, G.S. Pogosyan // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 51 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Zusammenfassung: | In the present work the classical problem of harmonic oscillator in the hyperbolic space H²₂: z²₀+z²₁−z²₂−z²₃=R² has been completely solved in framework of Hamilton-Jacobi equation. We have shown that the harmonic oscillator on H²₂, as in the other spaces with constant curvature, is exactly solvable and belongs to the class of maximally superintegrable system. We have proved that all the bounded classical trajectories are closed and periodic. The orbits of motion are ellipses or circles for bounded motion and ultraellipses or equidistant curve for infinite ones. |
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