Abstract
The analytical solution of The Klein Gordon equation was solved using the hypergeometry method for Hyperbolic Scarf plus Gendenstein III potential. The Klein Gordon equation for spin symmetry is reduced to the differential of one-dimensional Schrodinger-like equation. The wave function and the corresponding energy eigenvalues equation are simply obtained using variable separation and hypergeometric method. The numerical result of relativistic energy is calculated by Matlab R2013. These results can be applied to determines the thermodynamic's properties of the system such as vibrational mean-energy, vibrational specific heat , and vibrational mean-free energy.
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