The Green function G(x, y, z, t 0) (t r c) 4r is a solution of the inhomogeneous wave equation in three space dimensions with the source term (x)(y)(z)(t) (a) Show that G 2 (x, y, t) dz G(x, y, z, t) is a solution of the inhomogeneous wave equation in two space dimensions with the source term (x)(y)(t) (b) Evaluate the integral in part (a) to find G 2 (, t) explicitly, where 2 x 2 y 2

Question: The Green function G(x, y, z, t > 0) = (t r/c)/4r is a solution of the inhomogeneous wave equation in three space dimensions

The Green function G(x, y, z, t > 0) = δ(t − r/c)/4πr is a solution of the inhomogeneous wave equation in three space dimensions with the source term −δ(x)δ(y)δ(z)δ(t).
(a) Show that G₂(x, y, t) = ∫^∞_−∞dz G(x, y, z, t) is a solution of the inhomogeneous wave equation in two space dimensions with the source term −δ(x)δ(y)δ(t).
(b) Evaluate the integral in part (a) to find G₂(ρ, t) explicitly, where ρ²= x²+ y².

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