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.
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