The pedagogical value of the four-dimensional picture III: Solutions to Maxwell's equations

We outline a regular way for solving Maxwell's equations. We take, as the starting point, the notion of vector potentials. The rationale for introducing this notion in electrodynamics is that the set of Maxwell's equations is seemingly overdetermined. We demonstrate the existence of two fundamental solutions to Maxwell's equations whose linear combinations comprise the whole variety of classical electromagnetic field configurations.Comment: 11 page