Improved analytical approximation to arbitrary l-state solutions of the Schrodinger equation for the hyperbolical potentials

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IKHDAİR S., Sever R.

ANNALEN DER PHYSIK, vol.18, pp.747-758, 2009 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 18
  • Publication Date: 2009
  • Doi Number: 10.1002/andp.200910369
  • Journal Name: ANNALEN DER PHYSIK
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.747-758
  • Middle East Technical University Affiliated: Yes


The Schrodinger equation for the rotational-vibrational (ro-vibrational) motion of a diatomic molecule with empirical potential functions is solved approximately by means of the Nikiforov-Uvarov method. The approximate energy spectra and the corresponding normalized total wavefunctions are calculated in closed form and expressed in terms of the hypergeometric functions or Jacobi polynomials P-n((mu,nu)) (x), where mu > -1, nu > -1 and x is an element of[-1, +1]. The s-waves analytic solution is obtained. The numerical energy eigenvalues for selected H-2 and Ar-2 molecules are also calculated and compared with the previous models and experiments. (C) 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim