A relatively large amount of excellent work has been done during the past decade on general spectral and scattering theories for Schrodinger operators with long range oscillating potentials. However, most of these works do not include operators of the form where V is a short range potential. When V is radially symmetric, the problem has been successfully dealt with in recent years. On the other hand when V is not radially symmetric only one recent paper deals with these operators, but only for high energy values. In this paper we shall consider the spectral theory for this specific operator and compare our results with the previously mentioned paper.