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 J 0 (x) (ii) the regularization k 1 lim 0 k (k 2 2 ) and (iii) an integral representation of K 0 (x) For d 1, you will need (1 111) and the fundamental definition of the Green function

Question: 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

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 = lim_η→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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