Author(s):
Borrego-Morell, Jorge A. ; Bracciali, Cleonice F. [UNESP] ; Ranga, Alagacone Sri [UNESP]
Date: 2020
Persistent ID: http://hdl.handle.net/11449/200816
Origin: Oasisbr
Subject(s): Asymptotic expansions; Energy-dependent potential; Hypergeometric functions; Ordinary differential equations; Orthogonal polynomials; Schrödinger equation; Asymptotic expansions; Asymptotic expansions; Energy-dependent potential; Energy-dependent potential; Hypergeometric functions; Hypergeometric functions; Ordinary differential equations; Ordinary differential equations; Orthogonal polynomials; Orthogonal polynomials; Schrödinger equation; Schrödinger equation
Description
Made available in DSpace on 2020-12-12T02:16:50Z (GMT). No. of bitstreams: 0 Previous issue date: 2020-07-01
Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)
Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)
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.
Departamento de Matemática Campus Santa Cruz da Serra UFRJ-Universidade Federal do Rio de Janeiro
Departamento de Matemática Campus São José do Rio Preto UNESP-Universidade Estadual Paulista
Departamento de Matemática Campus São José do Rio Preto UNESP-Universidade Estadual Paulista
FAPESP: 2016/09906-0
CNPq: 304087/2018-1
CNPq: 402939/2016-6
