- 141 --


The solution of (8.12) is given by

                       r
               T(r) =    f (r')G(r,r')dr'           (8.15)


where the Green's function G(r,r') is the solution of


               L(r)G(r,r') = -6(r-r')               (8.16)

with boundary conditions G(O,r') = TO

                    G(R,r') = TR                    (8.17)

Morse and Feshbach (66) obtain an expression for G(r,r') by first solving the Poisson's equation in rectangular coordinates for the potential due to a point charge at (XV ty )
  (',Y'):


               V24(x,y)= -4Tr6(x-x')6(y-y')         (8.18)

The evaluation of G(r,r') using the solution to (8.18) is lengthy and only the pertinent details necessary for continuity will be outlined here. The solution to (8.18) is the Green's function G(xy; x'y') = knIz    z     = Re   zn(z-z')    z = x + iy(8.19)



Using a Taylor's series expansion for Zn(z-z')2,