Find the free-space Green functionG (d) 0 (r, r') in d = 1, 2, 3 space dimensions
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Find the free-space Green functionG(d)0 (r, r') in d = 1, 2, 3 space dimensions by the method of eigenfunction expansion. For d = 2, you will need (i) an integral representation of J0(x); (ii) the regularization k −1 = limη→0 k/(k2 + η2); and (iii) an integral representation of K0(x). For d = 1, you will need (1.111) and the fundamental definition of the Green function.
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In N dimensions the normalized eigenfunctions of V2 A are plane waves where k and r a...View the full answer
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