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Open Quantum Systems Decoherence Quantum Simulation Quantum State Preparation Representation

Rational extensions of the trigonometric Darboux-Pöschl-Teller potential based on para-Jacobi polynomials

arXiv
Authors: B. Bagchi, Y. Grandati, C. Quesne

Year

2014

Paper ID

46209

Status

Preprint

Abstract Read

~2 min

Abstract Words

100

Citations

N/A

Abstract

The possibility for the Jacobi equation to admit in some cases general solutions that are polynomials has been recently highlighted by Calogero and Yi, who termed them para-Jacobi polynomials. Such polynomials are used here to build seed functions of a Darboux-Bäcklund transformation for the trigonometric Darboux-Pöschl-Teller potential. As a result, one-step regular rational extensions of the latter depending both on an integer index n and on a continuously varying parameter λ are constructed. For each n value, the eigenstates of these extended potentials are associated with a novel family of λ-dependent polynomials, which are orthogonal on left] -1,1right[.

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  • The possibility for the Jacobi equation to admit in some cases general solutions that are polynomials has been recently highlighted by Calogero and Yi, who termed them...

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References & Citation Signals

[1] DOI https://doi.org/arXiv:1411.7857 [2] arXiv https://arxiv.org/abs/1411.7857 [3] Publisher https://arxiv.org/abs/1411.7857

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