  The analytic solutions of the spatially-dependent mass Schrodinger equation
of diatomic molecules with the centrifugal term l(l+1)/r2 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)=m0/(1-deltae^{-a(r-r_{e})})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 H2, LiH, HCl and CO
diatomic molecules are calculated and compared favourably well with those
obtained by using other approximation methods for arbitrary vibrational n and
rotational l quantum numbers.
