On Exact Solutions for a Luttinger Liquid with One Impurity

Reasons for the existence of exact solutions of the Luttinger model have been discussed. It has been shown that scattering by impurities at certain electron-electron coupling constants can be written in terms of Fermi quasiparticles exactly taking into account the electron-electron interaction. This circumstance significantly simplifies the analysis and in some cases leads to the existence of exact solutions.