Solutions of the Klein–Gordon equation with the Morse potential energy model in higher spatial dimensions

Abstract

We solve the Klein–Gordon equation with the Morse potential energy model to obtain the relativistic bound state energy equation in D spatial dimensions. We find that the inter-dimensional degeneracy symmetry exists for the molecular system represented by the Morse potential model. For a fixed vibrational quantum number and various rotational quantum numbers, the relativistic energies for the X1Σ+ state of the ScI molecule diverge as D increases. We observe that the behavior of the relativistic vibrational energies in higher dimensions remains similar to that of the three-dimensional system.