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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

On an Energy-Dependent Quantum System with Solutions in Terms of a Class of Hypergeometric Para-Orthogonal Polynomials on the Unit Circle

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Author(s):
Borrego-Morell, Jorge A. [1] ; Bracciali, Cleonice F. [2] ; Ranga, Alagacone Sri [2]
Total Authors: 3
Affiliation:
[1] UFRJ Univ Fed Rio de Janeiro, Dept Matemat, Campus Santa Cruz Serra, BR-25255030 Duque De Caxias, RJ - Brazil
[2] UNESP Univ Estadual Paulista, Dept Matemat, Campus Sao Jose do Rio Preto, BR-15054000 Sao Jose Do Rio Preto - Brazil
Total Affiliations: 2
Document type: Journal article
Source: MATHEMATICS; v. 8, n. 7 JUL 2020.
Web of Science Citations: 0
Abstract

We study an energy-dependent potential related to the Rosen-Morse potential. We give in closed-form the expression of a system of eigenfunctions of the Schrodinger operator in terms of a class of functions associated to a family of hypergeometric para-orthogonal polynomials on the unit circle. We also present modified relations of orthogonality and an asymptotic formula. Consequently, bound state solutions can be obtained for some values of the parameters that define the model. As a particular case, we obtain the symmetric trigonometric Rosen-Morse potential for which there exists an orthogonal basis of eigenstates in a Hilbert space. By comparing the existent solutions for the symmetric trigonometric Rosen-Morse potential, an identity involving Gegenbauer polynomials is obtained. (AU)

FAPESP's process: 16/09906-0 - Harmonic analysis, approximation theory and applications
Grantee:Dimitar Kolev Dimitrov
Support Opportunities: Research Projects - Thematic Grants