Scalar field equation in Schwarzschild space-time

The scalar field equation is reconsidered in the context of the Schwarzschild space-time. The solution is studied in the standard metric case by applying the usual separation method. The radial equation is interpreted, on general grounds, as an eigenvalue problem with associated scalar product. The difference is pointed out between that scalar product and the product induced on the radial solutions by the conserved current associated to the field equation. The explicit form of series solutions existing in the literature as well as the one proposed in the paper do not enable to solve the corresponding orthogonalization problem. The main properties of the solutions can however be obtained by transforming the radial equation into a wave equation with real potential. The structure of the potental function allows the discussion of some qualitative features of the motion of the particle.