Approximate solutions of the Schrödinger equation with the generalized Morse potential model including the centrifugal term

By using a new improved approximation scheme to deal with the centrifugal term, we solve approximately the Schrödinger equation with the generalized Morse potentials for the arbitrary angular momentum values. The bound state energy spectra and the unnormalized radial wave functions have been approximately obtained by using the basic concept of the supersymmetric shape invariance formalism and the function analysis method. The numerical experiments show that our approximate results are in better agreement with those obtained by using the numerical integration approach than the approximate results obtained by using the conventional approximation scheme to deal with the centrifugal term. We also calculate the rotational transition frequencies for HF molecule and compare them with the experimental data.