The quantization of the scalar field is reconsidered in some of its ba
sic elements in the context of the Robertson-Walker space-time. The in
tegration of the generalized Klein-Gordon equation is performed by pre
liminary separation of the equation with the usual separation method.
The orthonormal mode solutions are determined by the explicit integrat
ion of the resulting angular and radial equations and by standard prop
erties of the time equation. The time evolution given by the standard
cosmological model is briefly discussed.