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

Taseli H.

JOURNAL OF MATHEMATICAL CHEMISTRY, cilt.36, sa.1, ss.1-12, 2004 (SCI İndekslerine Giren Dergi) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 36 Konu: 1
  • Basım Tarihi: 2004
  • Doi Numarası: 10.1023/b:jomc.0000034929.23960.4e
  • Sayfa Sayıları: ss.1-12


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.