A Class of Orthogonal Polynomials Suggested by a Trigonometric Hamiltonian: Symmetric States

Byline: H. TaAeli (1) Keywords: Schrodinger equation; Exactly solvable hamiltonians; special functions; classical orthogonal polynomials Abstract: A new subclass of the Jacobi polynomials arising in the exact analytical solution of the one-dimensional Schrodinger equation with a trigonometric potential has been introduced. The polynomials which consist of a free parameter are not ultraspherical polynomials and have been simply named the T -polynomials since they are generated by a trigonometric Hamiltonian. In certain sense, it is shown that the T -polynomials can be regarded as a generalisation of the airfoil polynomials or the Chebyshev polynomials of the third kind. This paper is intended to discuss the basic properties of the polynomials so defined. Author Affiliation: (1) Department of Mathematics, Middle East Technical University, 06531, Ankara, Turkey Article History: Registration Date: 26/09/2004