In spherical coordinates, the delta function is tex2html_wrap215 .

The expansion of the angular portion of the delta function is: tex2html_wrap216 .

The laplacian can be expressed as tex2html_wrap217 where tex2html_wrap218

The Green's function will satisfy: tex2html_wrap219

Applying the poisson equation gives: tex2html_wrap220 where tex2html_wrap221 satisfies: tex2html_wrap222 . Then tex2html_wrap223 for tex2html_wrap224 and tex2html_wrap225 for tex2html_wrap226 .

Some algebra gives tex2html_wrap227

Integrating the equation for tex2html_wrap221 , you get: tex2html_wrap229 This means tex2html_wrap230 with tex2html_wrap231 .

This means tex2html_wrap232

tex2html_wrap233 .

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