Question: The Dirichlet Green function for any finite volume V can always be written in the form (a) Use the physical meaning of the Dirichlet Green

The Dirichlet Green function for any finite volume V can always be written in the form1 1 4 |rr| The function A (r, r') satisfies VA(r, r')

(a) Use the physical meaning of the Dirichlet Green function to prove that= 0. GD(r, r') = + A(r, r') r, r' V.

(b) Use Earnshaw’s theorem to prove that

1 1 4 |rr| The function A (r, r') satisfies VA(r, r') = 0. GD(r, r') = + A(r, r') r, r' V.

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