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

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