Rotation and vibration of diatomic molecule in the spatially-dependent mass Schrodinger equation with generalized q-deformed Morse potential

The analytic solutions of the spatially-dependent mass Schrodinger equation of diatomic molecules with the centrifugal term l(l + 1)/r(2) for the generalized q-deformed Morse potential are obtained approximately by means of a parametric generalization of the Nikiforov-Uvarov (NU) method combined with the Pekeris approximation scheme. The energy eigenvalues and the corresponding normalized radial wave functions are calculated in closed form with a physically motivated choice of a reciprocal Morse-like mass function, m(r) = m(0)/(1 - delta e(-a(r-re)))(2), 0 <= delta < 1, where a and r(e), are the range of the potential and the equilibrium position of the nuclei. The constant mass case when delta -> 0 is also studied. The energy states for H-2, LiH, HCl and CO diatomic molecules are calculated and compared favourably well with those obtained by using other approximation methods for arbitrary vibrationaln and rotational I quantum numbers. (C) 2009 Elsevier B.V. All rights reserved.