Ro-vibrating energy states of a diatomic molecule in an empirical potential

An approximate analytical solution of the Schrodinger equation is obtained to represent the rotational-vibrational (ro-vibrating) motion of a diatomic molecule. The ro-vibrating energy states arise from a systematical solution of the Schrodinger equation for an empirical potential (EP) V-+/-(r) = D-e{1-(epsilon/delta)[coth (eta r)](+/- 1)/1-(epsilon/delta)}(2) are determined by means of a mathematical method so-called the Nikiforov-Uvarov (NU). The effect of the potential parameters on the ro-vibrating energy states is discussed in several values of the vibrational and rotational quantum numbers. Moreover, the validity of the method is tested with previous models called the semiclassical (SC) procedure and the quantum mechanical (QM) method. The obtained results are applied to the molecules H-2 and Ar-2.