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Article Dans Une Revue Journal of Mathematical Physics Année : 2015

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

Résumé

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-Backlund transformation for the trigonometric Darboux-Poschl-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 lambda are constructed. For each n value, the eigenstates of these extended potentials are associated with a novel family of lambda-dependent polynomials, which are orthogonal on]-1,1[.
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Dates et versions

hal-01513176 , version 1 (09-05-2017)

Identifiants

Citer

B. Bagchi, Y. Grandati, C. Quesne. Rational extensions of the trigonometric Darboux-Poschl-Teller potential based on para-Jacobi polynomials. Journal of Mathematical Physics, 2015, 56 (6), pp.062103. ⟨10.1063/1.4922017⟩. ⟨hal-01513176⟩
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