  We discuss the Klein-Gordon (KG) equation using a 5D space-time approach. We
explicitly show that the KG equation in flat space-time admits a consistent
probabilistic interpretation with positively defined probability density.
However, the probabilistic interpretation is not covariant. In the
non-relativistic limit, the formalism reduces naturally to that of the
Schr\"odinger equation. We further discuss other interpretations of the KG
equation (and their non-relativistic limits) resulting from the 5D space-time
picture. Finally, we apply our results to the problem of hydrogenic spectra and
calculate the canonical sum of the hydrogenic atom.
