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Quantum Simulation Open Quantum Systems Decoherence Entanglement Theory Quantum Correlations

m-step rational extensions of the trigonometric Darboux-Pöschl-Teller potential based on para-Jacobi polynomials

arXiv
Authors: Yves Grandati, Christiane Quesne

Year

2024

Paper ID

38411

Status

Preprint

Abstract Read

~2 min

Abstract Words

80

Citations

N/A

Abstract

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 λ1, λ2, \ldots, λm, are obtained. The restrictions imposed on these parameters by the rational extensions regularity conditions are studied in detail.

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  • A previous construction of regular rational extensions of the trigonometric Darboux-Pöschl-Teller potential, obtained by one-step Darboux transformations using seed functions...

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References & Citation Signals

[1] DOI https://doi.org/arXiv:2410.05003 [2] arXiv https://arxiv.org/abs/2410.05003 [3] Publisher https://arxiv.org/abs/2410.05003

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