An exact solution of the Lippmann-Schwinger equation in one dimension

We consider a one-dimensional scattering problem and establish a system of two integral equations for the local (self-consistent) electric field. The equations are derived using the standard Green's function method. Their solution yields the local fields at any point of the system. To illustrate the efficacy of this approach, we apply it to a film and obtain analytical solutions that are identical to the Fabry-Perot solution. Some potential applications of the approach are also discussed.