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Symmetry, Integrability and Geometry: Methods and Applications, 2012, Volume 8, 074, 16 pp.
DOI: https://doi.org/10.3842/SIGMA.2012.074
(Mi sigma751)
 

This article is cited in 6 scientific papers (total in 6 papers)

Ladder operators for Lamé spheroconal harmonic polynomials

Ricardo Méndez-Fragosoa, Eugenio Ley-Koob

a Facultad de Ciencias, Universidad Nacional Autónoma de México, México
b Instituto de Física, Universidad Nacional Autónoma de México, México
Full-text PDF (575 kB) Citations (6)
References:
Abstract: 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 $n_1$ and $n_2$ counting the respective nodal elliptical cones. The second set of operators consisting of the cartesian components $\hat L_x$, $\hat L_y$, $\hat L_z$ 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 $\hat p_x$, $\hat p_y$, $\hat p_z$ 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.
Keywords: Lamé polynomials; spheroconal harmonics; ladder operators.
Received: July 31, 2012; in final form October 9, 2012; Published online October 17, 2012
Bibliographic databases:
Document Type: Article
Language: English
Citation: Ricardo Méndez-Fragoso, Eugenio Ley-Koo, “Ladder operators for Lamé spheroconal harmonic polynomials”, SIGMA, 8 (2012), 074, 16 pp.
Citation in format AMSBIB
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\by Ricardo M{\'e}ndez-Fragoso, Eugenio Ley-Koo
\paper Ladder operators for Lam\'e spheroconal harmonic polynomials
\jour SIGMA
\yr 2012
\vol 8
\papernumber 074
\totalpages 16
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  • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Symmetry, Integrability and Geometry: Methods and Applications
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