Supersymmetric Quantum Mechanics and Painlevé IV Equation
As it has been proven, the determination of general one-dimensional Schrödinger Hamiltonians having third-order differential ladder operators requires to solve the Painlevé IV equation. In this work, it will be shown that some specific subsets of the higher-order supersymmetric partners of the harmo...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2011 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2011
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/146780 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Supersymmetric Quantum Mechanics and Painlevé IV Equation / David Bermudez, David J. Fern'andez C. // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 27 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862580830389403648 |
|---|---|
| author | Bermudez, David Fern'andez C., David J. |
| author_facet | Bermudez, David Fern'andez C., David J. |
| citation_txt | Supersymmetric Quantum Mechanics and Painlevé IV Equation / David Bermudez, David J. Fern'andez C. // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 27 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | As it has been proven, the determination of general one-dimensional Schrödinger Hamiltonians having third-order differential ladder operators requires to solve the Painlevé IV equation. In this work, it will be shown that some specific subsets of the higher-order supersymmetric partners of the harmonic oscillator possess third-order differential ladder operators. This allows us to introduce a simple technique for generating solutions of the Painlevé IV equation. Finally, we classify these solutions into three relevant hierarchies.
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| first_indexed | 2025-11-26T20:27:10Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-146780 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-11-26T20:27:10Z |
| publishDate | 2011 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Bermudez, David Fern'andez C., David J. 2019-02-11T15:02:05Z 2019-02-11T15:02:05Z 2011 Supersymmetric Quantum Mechanics and Painlevé IV Equation / David Bermudez, David J. Fern'andez C. // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 27 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 81Q60; 35G20 DOI:10.3842/SIGMA.2011.025 https://nasplib.isofts.kiev.ua/handle/123456789/146780 As it has been proven, the determination of general one-dimensional Schrödinger Hamiltonians having third-order differential ladder operators requires to solve the Painlevé IV equation. In this work, it will be shown that some specific subsets of the higher-order supersymmetric partners of the harmonic oscillator possess third-order differential ladder operators. This allows us to introduce a simple technique for generating solutions of the Painlevé IV equation. Finally, we classify these solutions into three relevant hierarchies. This paper is a contribution to the Proceedings of the Workshop “Supersymmetric Quantum Mechanics and Spectral Design” (July 18–30, 2010, Benasque, Spain). The full collection is available at http://www.emis.de/journals/SIGMA/SUSYQM2010.html.
 The authors acknowledge the support of Conacyt. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Supersymmetric Quantum Mechanics and Painlevé IV Equation Article published earlier |
| spellingShingle | Supersymmetric Quantum Mechanics and Painlevé IV Equation Bermudez, David Fern'andez C., David J. |
| title | Supersymmetric Quantum Mechanics and Painlevé IV Equation |
| title_full | Supersymmetric Quantum Mechanics and Painlevé IV Equation |
| title_fullStr | Supersymmetric Quantum Mechanics and Painlevé IV Equation |
| title_full_unstemmed | Supersymmetric Quantum Mechanics and Painlevé IV Equation |
| title_short | Supersymmetric Quantum Mechanics and Painlevé IV Equation |
| title_sort | supersymmetric quantum mechanics and painlevé iv equation |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/146780 |
| work_keys_str_mv | AT bermudezdavid supersymmetricquantummechanicsandpainleveivequation AT fernandezcdavidj supersymmetricquantummechanicsandpainleveivequation |