Publicação: On an energy-dependent quantum system with solutions in terms of a class of hypergeometric para-orthogonal polynomials on the unit circle
Carregando...
Data
Orientador
Coorientador
Pós-graduação
Curso de graduação
Título da Revista
ISSN da Revista
Título de Volume
Editor
Tipo
Artigo
Direito de acesso
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.
Descrição
Palavras-chave
Asymptotic expansions, Energy-dependent potential, Hypergeometric functions, Ordinary differential equations, Orthogonal polynomials, Schrödinger equation
Idioma
Inglês
Como citar
Mathematics, v. 8, n. 7, 2020.
