  We review some results on the spectral theory of Schr{\"o}dinger and Dirac
operators. We focus on two aspects: the existence of embbedded eigen-values in
the essential spectrum and the limiting absorption principle. They both are
important for Physics, in general, and for Scattering theory, in particular. We
chose to include a special form of oscillations in the potential of the
considered operators to illustrate the diversity of behaviours that can exist
in the two selected topics. Concerning the limiting absorption principle, we
discuss several methods to prove it. To known, old or recent results, we added
some unpublished results from Mbarek's Phd Thesis.
