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



The Schrödinger 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 Pn(μ, ν) (x), where μ >−1, ν >−1 and x in [−1, +1]. The s-waves analytic solution is obtained. The numerical energy eigenvalues for selected H2 and Ar2 molecules are also calculated and compared with the previous models and experiments.