Expansion of the Greens function in eigen-functions

The spatial operator gf can be re-cast into the more familiar form of Chap. 7, Sect. 2 by first writing 

This operator is not self-adjoint. However, by writing P (r exp —ffC(r) eql /dr exp —jSI7(r)  

With this operator, the equation defining the Green s function is 

Following the usual procedure (see Morse and Feshbach [499]), the Green s function can be expanded in the eigen-functions pn 

Taking the Laplace transform of this and inserting into eqn, (275) gives 

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