# Approximate analytic solutions of the diatomic molecules in the Schrodinger equation with hyperbolical potentials - Quantum Physics

Abstract: The Schrodinger equation for the rotational-vibrational ro-vibrationalmotion 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, u}x, where\mu>-1, u>-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.

Author: Sameer M. Ikhdair, Ramazan Sever

Source: https://arxiv.org/