Lattice Green’s Function for the Simple Cubic Lattice

抄録

The lattice Green’s function of the simple cubic lattice
(Remark: Graphics omitted.)
is considered for the following ranges of the parameters;
t=s−iε, −∞<s<∞, 0≤l+m+n≤5.
The function G_sc(t;l, 0, 0) along an axis is expressed as a sum of simple integrals of the complete elliptic integral of the first kind and the integrals are evaluated numerically. The function G_sc(t;l, m, n) at a general position (l, m, n) is calculated with the aid of the recurrence formula which is satisfied by the Green’s function. The behaviors of the function G_sc(t;l, m, n) are shown by figures. Discussions of the divergent behavior of the derivative of G_sc(t;l, 0, 0) with respect to s, are given at the singular points, s=0, 1 and 3.