Free oscillator realization of Laguerre polynomials. (English. Russian original) Zbl 1493.34121
Theor. Math. Phys. 210, No. 1, 1-7 (2022); translation from Teor. Mat. Fiz. 210, No. 1, 3-10 (2022).
Summary: 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.
MSC:
| 34C15 | Nonlinear oscillations and coupled oscillators for ordinary differential equations |
| 34L15 | Eigenvalues, estimation of eigenvalues, upper and lower bounds of ordinary differential operators |
| 33C45 | Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) |
Keywords:
free oscillator realization; radial oscillator; Laguerre polynomial; harmonic oscillator; Hermite polynomialReferences:
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