Ladder Operators for Lamé Spheroconal Harmonic Polynomials
Three sets of ladder operators in spheroconal coordinates and their respective actions on Lamé spheroconal harmonic polynomials are presented in this article. The polynomials are common eigenfunctions of the square of the angular momentum operator and of the asymmetry distribution Hamiltonian for th...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2012 |
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| Sprache: | English |
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Інститут математики НАН України
2012
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/148705 |
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| Zitieren: | Ladder Operators for Lamé Spheroconal Harmonic Polynomials / R. Méndez-Fragoso, E. Ley-Koo // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 35 назв. — англ. |
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Méndez-Fragoso, R. Ley-Koo, E. 2019-02-18T18:03:21Z 2019-02-18T18:03:21Z 2012 Ladder Operators for Lamé Spheroconal Harmonic Polynomials / R. Méndez-Fragoso, E. Ley-Koo // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 35 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 20C35; 22E70; 33C47; 33C80; 81R05 DOI: http://dx.doi.org/10.3842/SIGMA.2012.074 https://nasplib.isofts.kiev.ua/handle/123456789/148705 Three sets of ladder operators in spheroconal coordinates and their respective actions on Lamé spheroconal harmonic polynomials are presented in this article. The polynomials are common eigenfunctions of the square of the angular momentum operator and of the asymmetry distribution Hamiltonian for the rotations of asymmetric molecules, in the body-fixed frame with principal axes. The first set of operators for Lamé polynomials of a given species and a fixed value of the square of the angular momentum raise and lower and lower and raise in complementary ways the quantum numbers n₁ and n₂ counting the respective nodal elliptical cones. The second set of operators consisting of the cartesian components Ĺx, Ĺy, Ĺz of the angular momentum connect pairs of the four species of polynomials of a chosen kind and angular momentum. The third set of operators, the cartesian components px, py, pz of the linear momentum, connect pairs of the polynomials differing in one unit in their angular momentum and in their parities. Relationships among spheroconal harmonics at the levels of the three sets of operators are illustrated. 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 authors express their appreciation to the organizers of the Symposium and editors of this Volume of SIGMA on “Superintegrability, Exact Solvability, and Special Functions” for their invitations to participate in both. The authors acknowledge the financial support for this work by Consejo Nacional de Ciencia y Tecnolog´ıa, SNI-1796. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Ladder Operators for Lamé Spheroconal Harmonic Polynomials Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Ladder Operators for Lamé Spheroconal Harmonic Polynomials |
| spellingShingle |
Ladder Operators for Lamé Spheroconal Harmonic Polynomials Méndez-Fragoso, R. Ley-Koo, E. |
| title_short |
Ladder Operators for Lamé Spheroconal Harmonic Polynomials |
| title_full |
Ladder Operators for Lamé Spheroconal Harmonic Polynomials |
| title_fullStr |
Ladder Operators for Lamé Spheroconal Harmonic Polynomials |
| title_full_unstemmed |
Ladder Operators for Lamé Spheroconal Harmonic Polynomials |
| title_sort |
ladder operators for lamé spheroconal harmonic polynomials |
| author |
Méndez-Fragoso, R. Ley-Koo, E. |
| author_facet |
Méndez-Fragoso, R. Ley-Koo, E. |
| publishDate |
2012 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| description |
Three sets of ladder operators in spheroconal coordinates and their respective actions on Lamé spheroconal harmonic polynomials are presented in this article. The polynomials are common eigenfunctions of the square of the angular momentum operator and of the asymmetry distribution Hamiltonian for the rotations of asymmetric molecules, in the body-fixed frame with principal axes. The first set of operators for Lamé polynomials of a given species and a fixed value of the square of the angular momentum raise and lower and lower and raise in complementary ways the quantum numbers n₁ and n₂ counting the respective nodal elliptical cones. The second set of operators consisting of the cartesian components Ĺx, Ĺy, Ĺz of the angular momentum connect pairs of the four species of polynomials of a chosen kind and angular momentum. The third set of operators, the cartesian components px, py, pz of the linear momentum, connect pairs of the polynomials differing in one unit in their angular momentum and in their parities. Relationships among spheroconal harmonics at the levels of the three sets of operators are illustrated.
|
| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/148705 |
| citation_txt |
Ladder Operators for Lamé Spheroconal Harmonic Polynomials / R. Méndez-Fragoso, E. Ley-Koo // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 35 назв. — англ. |
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AT mendezfragosor ladderoperatorsforlamespheroconalharmonicpolynomials AT leykooe ladderoperatorsforlamespheroconalharmonicpolynomials |
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2025-12-07T17:13:36Z |
| last_indexed |
2025-12-07T17:13:36Z |
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1850870455399874560 |