Stationary scattering theory

The older time dependent scattering theory was concerned with scattering waves and amplitudes, and was based on the Sommerfeld radiation condition and, when incorporated into the Schrodinger equation as a Cauchy condition at infinity, leads to the Lippmann-Schwinger equation. In the newer stationary scattering theory, solving the Lippmann-Schwinger equation leads to a linear map between generalized eigenfunctions of perturbed and unperturbed operators. This map is the section at fixed energy of the wave operator from the older time dependent theory. The radiation condition can be shown to hold, a posteriori, in many situations, thus the link with prior physical theories