Geodesic
Free oscillator realization of Laguerre polynomials
Teoretičeskaâ i matematičeskaâ fizika, Tome 210 (2022) no. 1, pp. 3-10 Cet article a éte moissonné depuis la source Math-Net.Ru

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We revisit the radial oscillator from the standpoint of a free oscillator realization. By using a free oscillator, namely, the creation/annihilation operators of the harmonic oscillator, we construct an operator that maps the eigenfunctions of the harmonic oscillator to those of the radial oscillator. As a polynomial part of this relation, we obtain an operator that maps the Hermite polynomials to the Laguerre polynomials.
Keywords: free oscillator realization, radial oscillator, harmonic oscillator
Mots-clés : Laguerre polynomial, Hermite polynomial. 
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S. Odake. Free oscillator realization of Laguerre polynomials. Teoretičeskaâ i matematičeskaâ fizika, Tome 210 (2022) no. 1, pp. 3-10. http://geodesic.mathdoc.fr/item/TMF_2022_210_1_a0/

[1] S. Odake, “Beyond CFT: Deformed Virasoro and elliptic algebras”, Theoretical Physics at the End of the Twentieth Century, Proceedings of the 9th CRM Summer School (Banff, Canada, June 27–July 10, 1999), eds. Y. Saint-Aubin, L. Vinet, Springer, New York, 2002, 307–449, arXiv: hep-th/9910226 | Zbl

[2] F. Cooper, A. Khare, U. Sukhatme, “Supersymmetry and quantum mechanics”, Phys. Rep., 251:5–6 (1995), 267–385, arXiv: hep-th/9405029 | DOI

[3] R. Koekoek, P. A. Lesky, R. F. Swarttouw, Hypergeometric Orthogonal Polynomials and Their $q$-Analogues, Springer Monographs in Mathematics, Springer, Berlin, 2010 | DOI

[4] S. Odake, R. Sasaki, “Exactly solvable quantum mechanics and infinite families of multi-indexed orthogonal polynomials”, Phys. Lett. B, 702:2–3 (2011), 164–170, arXiv: 1105.0508 | DOI