Bound State Solutions of the Schr\"odinger Equation for Generalized Morse Potential With Position Dependent Mass

The effective mass one-dimensional Schr"odinger equation for the generalized Morse potential is solved by using Nikiforov-Uvarov method. Energy eigenvalues and corresponding eigenfunctions are computed analytically. The results are also reduced to the case of constant mass. Energy eigenvalues are computed numerically for some diatomic molecules. The results are in agreement with the ones obtained before.