Harmonic Oscillator SUSY Partners and Evolution Loops
Supersymmetric quantum mechanics is a powerful tool for generating exactly solvable potentials departing from a given initial one. If applied to the harmonic oscillator, a family of Hamiltonians ruled by polynomial Heisenberg algebras is obtained. In this paper it will be shown that the SUSY partner...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2012 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2012
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/148452 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Harmonic Oscillator SUSY Partners and Evolution Loops / D.J. Fernández // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 60 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862747526671630336 |
|---|---|
| author | Fernández, D.J. |
| author_facet | Fernández, D.J. |
| citation_txt | Harmonic Oscillator SUSY Partners and Evolution Loops / D.J. Fernández // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 60 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | Supersymmetric quantum mechanics is a powerful tool for generating exactly solvable potentials departing from a given initial one. If applied to the harmonic oscillator, a family of Hamiltonians ruled by polynomial Heisenberg algebras is obtained. In this paper it will be shown that the SUSY partner Hamiltonians of the harmonic oscillator can produce evolution loops. The corresponding geometric phases will be as well studied.
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| first_indexed | 2025-12-07T20:51:39Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-148452 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T20:51:39Z |
| publishDate | 2012 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Fernández, D.J. 2019-02-18T12:55:27Z 2019-02-18T12:55:27Z 2012 Harmonic Oscillator SUSY Partners and Evolution Loops / D.J. Fernández // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 60 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 81Q60; 81Q05; 81Q70 DOI: http://dx.doi.org/10.3842/SIGMA.2012.041 https://nasplib.isofts.kiev.ua/handle/123456789/148452 Supersymmetric quantum mechanics is a powerful tool for generating exactly solvable potentials departing from a given initial one. If applied to the harmonic oscillator, a family of Hamiltonians ruled by polynomial Heisenberg algebras is obtained. In this paper it will be shown that the SUSY partner Hamiltonians of the harmonic oscillator can produce evolution loops. The corresponding geometric phases will be as well studied. 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.
 The author acknowledges the financial support of Conacyt, project 152574, as well as the comments of Alonso Contreras-Astorga. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Harmonic Oscillator SUSY Partners and Evolution Loops Article published earlier |
| spellingShingle | Harmonic Oscillator SUSY Partners and Evolution Loops Fernández, D.J. |
| title | Harmonic Oscillator SUSY Partners and Evolution Loops |
| title_full | Harmonic Oscillator SUSY Partners and Evolution Loops |
| title_fullStr | Harmonic Oscillator SUSY Partners and Evolution Loops |
| title_full_unstemmed | Harmonic Oscillator SUSY Partners and Evolution Loops |
| title_short | Harmonic Oscillator SUSY Partners and Evolution Loops |
| title_sort | harmonic oscillator susy partners and evolution loops |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/148452 |
| work_keys_str_mv | AT fernandezdj harmonicoscillatorsusypartnersandevolutionloops |