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The scattering state solutions of the Klein-Gordon equation with equal scalarand vector Varshni, Hellmann and Varshni-Shukla potentials for any arbitraryangular momentum quantum number l are investigated within the framework of thefunctional analytical method using a suitable approximation. The asymptoticwave functions, approximate scattering phase shifts, normalization constantsand bound state energy equations were obtained. The non-relativistic limits ofthe scattering phase shifts and the bound states energy equations for the threepotentials were also obtained. Our bound states energy equations are inexcellent agreement with the available ones in the literature. Our numericaland graphical results indicate the dependence of phase shifts on the screeningparameter \b{eta}, the potential parameter b and angular momentum quantumnumber l.

Scattering states solutions of Klein-Gordon equation with three physically solvable potential models