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We present an approximate analytic solution of the Klein-Gordon equation inthe presence of equal scalar and vector generalized deformed hyperbolicpotential functions by means of parameteric generalization of theNikiforov-Uvarov method. We obtain the approximate bound staterotational-vibrational (ro-vibrational) energy levels and the correspondingnormalized wave functions expressed in terms of the Jacobi polynomial for aspin-zero particle in a closed form. Special cases are studied including thenon-relativistic solutions obtained by appropriate choice of parameters andalso the s-wave solutions.

Rotational and vibrational diatomic molecule in the Klein-Gordon equation with hyperbolic scalar and vector potentials