ROTATIONAL AND VIBRATIONAL DIATOMIC MOLECULE IN THE KLEIN GORDON EQUATION WITH HYPERBOLIC SCALAR AND VECTOR POTENTIALS

We present an approximate analytic solution of the Klein Gordon equation in the presence of equal scalar and vector generalized deformed hyperbolic potential functions by means of parametric generalization of the Nikiforov-Uvarov method. We obtain the approximate bound-state rotational vibrational (ro-vibrational) energy levels and the corresponding normalized wave functions expressed in terms of the Jacobi polynomial Pn((mu,v)) (x), where mu > -1, v > -1, and x is an element of [-1, +1] for a spin-zero particle in a closed form. Special cases are studied including the nonrelativistic solutions obtained by appropriate choice of parameters and also the s-wave solutions.