The rotating Morse potential energy eigenvalues solved by using the analytical transfer matrix method

We study the eigenvalues of the rotating Morse potential by using the quantization condition from the analytical transfer matrix (ATM) method. A hierarchy of supersymmetric partner potentials is obtained with Pekeris approximation, which can be used to calculate the energies of higher rotational states from the energies of lower states. The energies of rotational states of the hydrogen molecule are calculated by the ATM condition, and comparison of the results with those from the hypervirial perturbation method reveals that the accuracy of the approximate expression of Pekeris for the eigenvalues of the rotating Morse potential can be improved substantially in the framework of supersymmetric quantum mechanics.