-A simplified model Hamiltonian is presented and applied to calculate the density of magnetic impurity states and to study the formation of local magnetic moments in a non-magnetic host metal when a small amount of magnetic impurities is dissolved in it. For this purpose, the many-body Anderson impurity Hamiltonian is transformed into an effective one-body Hamiltonian within the framework of second quantization.This Hamiltonian is then used to derive the equations of motion for the double-time retarded Green's functions in Zubarev's notation. These Green''s functions are employed to calculate the density of impurity states and the average occupation number of impurity electrons with specific spin orientations. Finally the general magnetic solutions are found and a phase diagram is drawn to show how local magnetic moments may be formed under suitable conditions determined by an intricate interplay of certain physical parameters such as impurity energy levels, on-site coulomb repulsion and the hybridization energy.