Geodesic
Free oscillator realization of Laguerre polynomials
Teoretičeskaâ i matematičeskaâ fizika, Tome 210 (2022) no. 1, pp. 3-10

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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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     author = {S. Odake},
     title = {Free oscillator realization of {Laguerre} polynomials},
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     publisher = {mathdoc},
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     url = {http://geodesic.mathdoc.fr/item/TMF_2022_210_1_a0/}
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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/