Abstract
We solve the Klein-Gordon equation with the simplified Poschl-Teller potential model by employing the shape invariance technique, and present the relativistic spinless rotation-vibrational energy equation for diatomic molecules with nuclear spin of zero. It is found that the relativistic effects subject to the relative motion of the ions increase slightly the spinless vibrational energies of the ground electronic state of the carbon monoxide molecule in comparison to the nonrelativistic results. We observe that the variation of the relativistic spinless rotation-vibrational energies with respect to the vibrational quantum number in larger rotational quantum numbers holds similar to that with rotational quantum number of zero.
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