Related papers: Rationally-extended Dunkl oscillator on the line

Rationally-extended Dunkl oscillator on the line

URL: http://arxiv.org/abs/2304.05846v2
Date: Fri, 9 Jun 2023 12:28:12 GMT
Title: Rationally-extended Dunkl oscillator on the line
Authors: C. Quesne
Abstract summary: It is shown that the extensions of exactly-solvable quantum mechanical problems connected with the replacement of ordinary derivatives by Dunkl ones can be easily combined.
Score: 0.0
License: http://creativecommons.org/licenses/by/4.0/
Abstract: It is shown that the extensions of exactly-solvable quantum mechanical problems connected with the replacement of ordinary derivatives by Dunkl ones and with that of classical orthogonal polynomials by exceptional orthogonal ones can be easily combined. For such a purpose, the example of the Dunkl oscillator on the line is considered and three different types of rationally-extended Dunkl oscillators are constructed. The corresponding wavefunctions are expressed in terms of exceptional orthogonal generalized Hermite polynomials, defined in terms of the three different types of $X_m$-Laguerre exceptional orthogonal polynomials. Furthermore, the extended Dunkl oscillator Hamiltonians are shown to be expressible in terms of some extended Dunkl derivatives and some anharmonic oscillator potentials.

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