Singular Isotonic Oscillator, Supersymmetry and Superintegrability
In the case of a one-dimensional nonsingular Hamiltonian H and a singular supersymmetric partner Hα, the Darboux and factorization relations of supersymmetric quantum mechanics can be only formal relations. It was shown how we can construct an adequate partner by using infinite barriers placed where...
Збережено в:
| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Дата: | 2012 |
| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2012
|
| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/148465 |
| 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: | Singular Isotonic Oscillator, Supersymmetry and Superintegrability / I. Marquette // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 47 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862701356533415936 |
|---|---|
| author | Marquette, I. |
| author_facet | Marquette, I. |
| citation_txt | Singular Isotonic Oscillator, Supersymmetry and Superintegrability / I. Marquette // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 47 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | In the case of a one-dimensional nonsingular Hamiltonian H and a singular supersymmetric partner Hα, the Darboux and factorization relations of supersymmetric quantum mechanics can be only formal relations. It was shown how we can construct an adequate partner by using infinite barriers placed where are located the singularities on the real axis and recover isospectrality. This method was applied to superpartners of the harmonic oscillator with one singularity. In this paper, we apply this method to the singular isotonic oscillator with two singularities on the real axis. We also applied these results to four 2D superintegrable systems with second and third-order integrals of motion obtained by Gravel for which polynomial algebras approach does not allow to obtain the energy spectrum of square integrable wavefunctions. We obtain solutions involving parabolic cylinder functions.
|
| first_indexed | 2025-12-07T16:42:04Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-148465 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T16:42:04Z |
| publishDate | 2012 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Marquette, I. 2019-02-18T13:19:28Z 2019-02-18T13:19:28Z 2012 Singular Isotonic Oscillator, Supersymmetry and Superintegrability / I. Marquette // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 47 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 81R15; 81R12; 81R50 DOI: http://dx.doi.org/10.3842/SIGMA.2012.063 https://nasplib.isofts.kiev.ua/handle/123456789/148465 In the case of a one-dimensional nonsingular Hamiltonian H and a singular supersymmetric partner Hα, the Darboux and factorization relations of supersymmetric quantum mechanics can be only formal relations. It was shown how we can construct an adequate partner by using infinite barriers placed where are located the singularities on the real axis and recover isospectrality. This method was applied to superpartners of the harmonic oscillator with one singularity. In this paper, we apply this method to the singular isotonic oscillator with two singularities on the real axis. We also applied these results to four 2D superintegrable systems with second and third-order integrals of motion obtained by Gravel for which polynomial algebras approach does not allow to obtain the energy spectrum of square integrable wavefunctions. We obtain solutions involving parabolic cylinder functions. This paper is a contribution to the Special Issue “Superintegrability, Exact Solvability, and Special Functions”. The full collection is available at http://www.emis.de/journals/SIGMA/SESSF2012.html.
 This work was supported by the Australian Research Council through Discovery Project
 DP110101414. The article was written in part while he was visiting the Universite Libres de Bruxelles. He thanks C. Quesne for her hospitality. He thanks the FNRS for a travel fellowship. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Singular Isotonic Oscillator, Supersymmetry and Superintegrability Article published earlier |
| spellingShingle | Singular Isotonic Oscillator, Supersymmetry and Superintegrability Marquette, I. |
| title | Singular Isotonic Oscillator, Supersymmetry and Superintegrability |
| title_full | Singular Isotonic Oscillator, Supersymmetry and Superintegrability |
| title_fullStr | Singular Isotonic Oscillator, Supersymmetry and Superintegrability |
| title_full_unstemmed | Singular Isotonic Oscillator, Supersymmetry and Superintegrability |
| title_short | Singular Isotonic Oscillator, Supersymmetry and Superintegrability |
| title_sort | singular isotonic oscillator, supersymmetry and superintegrability |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/148465 |
| work_keys_str_mv | AT marquettei singularisotonicoscillatorsupersymmetryandsuperintegrability |