# The Green function G(x, y, z, t > 0) = (t r/c)/4r is a solution of

## Question:

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 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 −δ(x)δ(y)δ(t).

(b) Evaluate the integral in part (a) to find G_{2}(ρ, t) explicitly, where ρ^{2 }= x^{2 }+ y^{2}.

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