M. Fabbrichesi , SISSA

The wave equation

The first part of this lesson concerns the definitions of vector and scalar potential. Maxwell equations are rewritten in terms of these quantities. The concept of gauge-invariance is introduced and the Lorentz gauge is discussed [Jackson sect. 6.2 - 6.3].

The second part of this lesson is devoted to the Green functions of the wave equation (see Jackson sect. 6.4). Definitions and meaning of the retarded and advanced Green functions are discussed. Complete solutions of the inhomogeneous wave equation are given in terms of the retarded and advanced Green functions.