In Chapter 5, I showed that it is always possible to pick a vector potential whose diver...

In Chapter 5, I showed that it is always possible to pick a vector potential whose divergence is zero (the Coulomb gauge). Show that it is always possible to choose as required for the Lorenz gauge, assuming you know how to solve the inhomogeneous wave equation (Eq. 10.16). Is it always possible to pick V = 0? How about A = 0?

Reference equation 10.16