$m$-step rational extensions of the trigonometric Darboux-Pöschl-Teller potential based on para-Jacobi polynomials
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866909842649645056 |
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| author | Grandati, Yves Quesne, Christiane |
| author_facet | Grandati, Yves Quesne, Christiane |
| contents | A previous construction of regular rational extensions of the trigonometric Darboux-Pöschl-Teller potential, obtained by one-step Darboux transformations using seed functions associated with the para-Jacobi polynomials of Calogero and Yi, is generalized by considering $m$-step Darboux transformations. As a result, some novel families of exceptional orthogonal polynomials depending on $m$ discrete parameters, as well as $m$ continuous real ones $λ_1$, $λ_2$, \ldots, $λ_m$, are obtained. The restrictions imposed on these parameters by the rational extensions regularity conditions are studied in detail. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_05003 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | $m$-step rational extensions of the trigonometric Darboux-Pöschl-Teller potential based on para-Jacobi polynomials Grandati, Yves Quesne, Christiane Mathematical Physics Exactly Solvable and Integrable Systems Quantum Physics A previous construction of regular rational extensions of the trigonometric Darboux-Pöschl-Teller potential, obtained by one-step Darboux transformations using seed functions associated with the para-Jacobi polynomials of Calogero and Yi, is generalized by considering $m$-step Darboux transformations. As a result, some novel families of exceptional orthogonal polynomials depending on $m$ discrete parameters, as well as $m$ continuous real ones $λ_1$, $λ_2$, \ldots, $λ_m$, are obtained. The restrictions imposed on these parameters by the rational extensions regularity conditions are studied in detail. |
| title | $m$-step rational extensions of the trigonometric Darboux-Pöschl-Teller potential based on para-Jacobi polynomials |
| topic | Mathematical Physics Exactly Solvable and Integrable Systems Quantum Physics |
| url | https://arxiv.org/abs/2410.05003 |