A class of orthogonal polynomials suggested by a trigonometric Hamiltonian : Symmetric states


Taseli H.

JOURNAL OF MATHEMATICAL CHEMISTRY, vol.36, no.1, pp.1-12, 2004 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 36 Issue: 1
  • Publication Date: 2004
  • Doi Number: 10.1023/b:jomc.0000034929.23960.4e
  • Title of Journal : JOURNAL OF MATHEMATICAL CHEMISTRY
  • Page Numbers: pp.1-12

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.