Singular Isotonic Oscillator, Supersymmetry and Superintegrability
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
Singular Isotonic Oscillator, Supersymmetry and Superintegrability
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| Creator |
Marquette, I.
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| 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.
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| Date |
2019-02-18T13:19:28Z
2019-02-18T13:19:28Z 2012 |
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| Type |
Article
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| Identifier |
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 http://dspace.nbuv.gov.ua/handle/123456789/148465 |
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| Language |
en
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| Relation |
Symmetry, Integrability and Geometry: Methods and Applications
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| Publisher |
Інститут математики НАН України
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