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...
Збережено в:
| Дата: | 2015 |
|---|---|
| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2015
|
| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/147158 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-147158 |
|---|---|
| record_format |
dspace |
| spelling |
irk-123456789-1471582019-02-14T01:24:48Z Harmonic Oscillator on the SO(2,2) Hyperboloid Petrosyan, D.R. Pogosyan, G.S. 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. 2015 Article 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. 1815-0659 2010 Mathematics Subject Classification: 22E60; 37J15; 37J50; 70H20 DOI:10.3842/SIGMA.2015.096 http://dspace.nbuv.gov.ua/handle/123456789/147158 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
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. |
| format |
Article |
| author |
Petrosyan, D.R. Pogosyan, G.S. |
| spellingShingle |
Petrosyan, D.R. Pogosyan, G.S. Harmonic Oscillator on the SO(2,2) Hyperboloid Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Petrosyan, D.R. Pogosyan, G.S. |
| author_sort |
Petrosyan, D.R. |
| title |
Harmonic Oscillator on the SO(2,2) Hyperboloid |
| title_short |
Harmonic Oscillator on the SO(2,2) Hyperboloid |
| title_full |
Harmonic Oscillator on the SO(2,2) Hyperboloid |
| title_fullStr |
Harmonic Oscillator on the SO(2,2) Hyperboloid |
| title_full_unstemmed |
Harmonic Oscillator on the SO(2,2) Hyperboloid |
| title_sort |
harmonic oscillator on the so(2,2) hyperboloid |
| publisher |
Інститут математики НАН України |
| publishDate |
2015 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/147158 |
| citation_txt |
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. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT petrosyandr harmonicoscillatorontheso22hyperboloid AT pogosyangs harmonicoscillatorontheso22hyperboloid |
| first_indexed |
2023-05-20T17:26:44Z |
| last_indexed |
2023-05-20T17:26:44Z |
| _version_ |
1796153311718539264 |