  The interest in the Klein-Gordon equation with different potentials has
increased in recent years due to its possible applications in Cosmology, Hadron
Physics and High-Energy Physics. In this work we investigate the solutions of
the Klein-Gordon equation for bosons under the influence of an external
potential by using the Feshbach-Villars method. We present detailed results for
two cases: the Coulombic potential and the harmonic potential. For the latter
case, we studied the effects of self-interacting particles by adopting a
mean-field approach. We show that our results converge smoothly to the solution
of the Schr\"odinger equation for the same systems as the relativistic effects
diminish.
