Solvable Rational Potentials and Exceptional Orthogonal Polynomials in Supersymmetric Quantum Mechanics
New exactly solvable rationally-extended radial oscillator and Scarf I potentials are generated by using a constructive supersymmetric quantum mechanical method based on a reparametrization of the corresponding conventional superpotential and on the addition of an extra rational contribution express...
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| Дата: | 2009 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2009
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/149120 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Solvable Rational Potentials and Exceptional Orthogonal Polynomials in Supersymmetric Quantum Mechanics / C. Quesne // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 38 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
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irk-123456789-1491202019-02-20T01:25:32Z Solvable Rational Potentials and Exceptional Orthogonal Polynomials in Supersymmetric Quantum Mechanics Quesne, C. New exactly solvable rationally-extended radial oscillator and Scarf I potentials are generated by using a constructive supersymmetric quantum mechanical method based on a reparametrization of the corresponding conventional superpotential and on the addition of an extra rational contribution expressed in terms of some polynomial g. The cases where g is linear or quadratic are considered. In the former, the extended potentials are strictly isospectral to the conventional ones with reparametrized couplings and are shape invariant. In the latter, there appears a variety of extended potentials, some with the same characteristics as the previous ones and others with an extra bound state below the conventional potential spectrum. Furthermore, the wavefunctions of the extended potentials are constructed. In the linear case, they contain (ν+1)th-degree polynomials with ν = 0,1,2,..., which are shown to be X1-Laguerre or X1-Jacobi exceptional orthogonal polynomials. In the quadratic case, several extensions of these polynomials appear. Among them, two different kinds of (ν+2)th-degree Laguerre-type polynomials and a single one of (ν+2)th-degree Jacobi-type polynomials with ν = 0,1,2,... are identified. They are candidates for the still unknown X2-Laguerre and X2-Jacobi exceptional orthogonal polynomials, respectively. 2009 Article Solvable Rational Potentials and Exceptional Orthogonal Polynomials in Supersymmetric Quantum Mechanics / C. Quesne // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 38 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 33E30; 81Q05; 81Q60 http://dspace.nbuv.gov.ua/handle/123456789/149120 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 |
New exactly solvable rationally-extended radial oscillator and Scarf I potentials are generated by using a constructive supersymmetric quantum mechanical method based on a reparametrization of the corresponding conventional superpotential and on the addition of an extra rational contribution expressed in terms of some polynomial g. The cases where g is linear or quadratic are considered. In the former, the extended potentials are strictly isospectral to the conventional ones with reparametrized couplings and are shape invariant. In the latter, there appears a variety of extended potentials, some with the same characteristics as the previous ones and others with an extra bound state below the conventional potential spectrum. Furthermore, the wavefunctions of the extended potentials are constructed. In the linear case, they contain (ν+1)th-degree polynomials with ν = 0,1,2,..., which are shown to be X1-Laguerre or X1-Jacobi exceptional orthogonal polynomials. In the quadratic case, several extensions of these polynomials appear. Among them, two different kinds of (ν+2)th-degree Laguerre-type polynomials and a single one of (ν+2)th-degree Jacobi-type polynomials with ν = 0,1,2,... are identified. They are candidates for the still unknown X2-Laguerre and X2-Jacobi exceptional orthogonal polynomials, respectively. |
| format |
Article |
| author |
Quesne, C. |
| spellingShingle |
Quesne, C. Solvable Rational Potentials and Exceptional Orthogonal Polynomials in Supersymmetric Quantum Mechanics Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Quesne, C. |
| author_sort |
Quesne, C. |
| title |
Solvable Rational Potentials and Exceptional Orthogonal Polynomials in Supersymmetric Quantum Mechanics |
| title_short |
Solvable Rational Potentials and Exceptional Orthogonal Polynomials in Supersymmetric Quantum Mechanics |
| title_full |
Solvable Rational Potentials and Exceptional Orthogonal Polynomials in Supersymmetric Quantum Mechanics |
| title_fullStr |
Solvable Rational Potentials and Exceptional Orthogonal Polynomials in Supersymmetric Quantum Mechanics |
| title_full_unstemmed |
Solvable Rational Potentials and Exceptional Orthogonal Polynomials in Supersymmetric Quantum Mechanics |
| title_sort |
solvable rational potentials and exceptional orthogonal polynomials in supersymmetric quantum mechanics |
| publisher |
Інститут математики НАН України |
| publishDate |
2009 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/149120 |
| citation_txt |
Solvable Rational Potentials and Exceptional Orthogonal Polynomials in Supersymmetric Quantum Mechanics / C. Quesne // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 38 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT quesnec solvablerationalpotentialsandexceptionalorthogonalpolynomialsinsupersymmetricquantummechanics |
| first_indexed |
2023-05-20T17:32:22Z |
| last_indexed |
2023-05-20T17:32:22Z |
| _version_ |
1796153522225414144 |