Application of quantum supersymmetry to rovibrational states of diatomic molecules with an energy dependent Morse potential

Abstract

The energy-dependent Morse potential is used to study diatomic molecules. Their rovibrational energy eigenvalues are calculated by applying the quantum supersymmetry (SUSY-QM) formalism related to this kind of potentials associated to the Pekeris approximation of the centrifugal term. At first, a general case with this energy dependent potential is investigated in order to test the efficiency of the Pekeris approximation in function of the potential range parameter. A comparison between the obtained analytical results with the exact numerical solutions of the Schrödinger equation in the energy-dependent and the energy-independent cases shows that the numerical results agree well with the analytical expression. An other point is also verified, the curve shape of the potential behavior is studied and compared with the standard Morse potential form and the Rydberg Klein Rees (RKR) data in the case of the ground state of the two diatomic molecules: N2 and O2. The solubility of the general proposed model and the compatibility of the ground energy dependent potential with the RKR data curves represent the key elements that led us to make an extension of this study to realistic cases. Applications of SUSY-QM to some several diatomic molecules: N2, O2, Li2 and HF are shown the effect of this dependence on their rovibrational energy spectra