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

The analytic solutions of the spatially-dependent mass Schrödinger 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-δe-a(r-re))2,0⩽δ<1, where a and re are the range of the potential and the equilibrium position of the nuclei. The constant mass case when δ→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 vibrationaln and rotational l quantum numbers.