  A first order differential equation of Green's Function, at the origin G(0),
for the one- dimensional lattice is derived by simple recurrence relation.
Green's Function at site (m)is then calculated in terms of G(0). A simple
recurrence relation connecting the lattice Green's Function at the site
(m,n)and the first derivative of the lattice Green's Function at the site
(m+_1,n)is presented for the two- dimensional lattice, a differential equation
of the second order in G(0,0) is obtained. By making use of the letter
recurrence relation, lattice Green's Function at an arbitrary site is obtained
in closed form. Finally, the phase shift and scattering cross section are
evaluated analytically and numerically for one- and two impurities.
