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

Autor(es)

Borrego-Morell, Jorge A. ^[1] ; Bracciali, Cleonice F. ^[2] ; Ranga, Alagacone Sri ^[2]

Afiliação do(s) autor(es)

^[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

• Tipo de documento: Artigo Científico
• Fonte: MATHEMATICS; v. 8, n. 7 JUL 2020.
• Citações Web of Science: 0

Resumo

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)

• Processo FAPESP: 16/09906-0 - Análise harmônica, teoria da aproximação, funções especiais e aplicações
• Beneficiário: Dimitar Kolev Dimitrov
• Modalidade de apoio: Auxílio à Pesquisa - Temático