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


Taseli H.

JOURNAL OF MATHEMATICAL CHEMISTRY, cilt.37, ss.377-388, 2005 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 37 Konu: 4
  • Basım Tarihi: 2005
  • Doi Numarası: 10.1007/s10910-004-1104-1
  • Dergi Adı: JOURNAL OF MATHEMATICAL CHEMISTRY
  • Sayfa Sayıları: ss.377-388

Özet

This is the second in a series of papers dealing with the sets of orthogonal polynomials generated by a trigonometric Hamiltonian. In the first of this series, a subclass of the Jacobi polynomials denoted by T-n((u)) (x) and referred to as the T - polynomial of the first kind, which arises in the investigation of the symmetric state eigenfunctions of the Hamiltonian under consideration, was examined. Another subclass of the Jacobi polynomials denoted by U ((u))(n) (x) is introduced here representing the antisymmetric states, and is called in accordance the T - polynomial of the second kind. Moreover, by the derivation of the ultraspherical polynomial wavefunctions, interrelations between the T - polynomials of the first and second kinds as well as the other orthogonal polynomial systems are also emphasized.