G ( x , x ′ ) = i 4 H 0 ( 1 ) ( k | x − − x ′ | ) for n = 2, where H 0 is a Hankel function, and G ( x , x ′ ) = e i k | x − − x ′ | 4 π π | x − − x ′ | for n = 3. Note that we have chosen the boundary condition that the Green's function is an outgoing wave for | x | → ∞.