Approximate analytic solutions of the diatomic molecules in the Schrodinger equation with hyperbolical potentials

摘要

The Schrodinger equation for the rotational-vibrational (ro-vibrational)motion of a diatomic molecule with empirical potential functions is solvedapproximately by means of the Nikiforov-Uvarov method. The approximatero-vibratinal energy spectra and the corresponding normalized totalwavefunctions are calculated in closed form and expressed in terms of thehypergeometric functions or Jacobi polynomials P_{n}^{(\mu,\nu)}(x), where\mu>-1, \nu>-1 and x included in [-1,+1]. The s-waves analytic solution isobtained. The numerical energy eigenvalues for selected H_{2} and Ar_{2}molecules are also calculated and compared with the previous models andexperiments.