ADDITIONAL BOUNDARY-CONDITIONS - AN HISTORICAL MISTAKE

Since their introduction by Pekar in 1956, additional boundary conditi ons (ABC's) have been used in innumerable papers and in different ways to calculate the reflectivity for frequencies where more than one wav e can propagate in a dielectric medium, particularly in connection wit h the polariton problem. Regarding the surface as a source of radiatio n into the medium this long lasting problem is removed demonstrating a unique solution to exist if, as usually assumed, the thickness of the surface layer is small compared with the wavelength. The analysis app lies to any medium described by a dielectric function epsilon(q,omega) . Half-space and slab geometry are studied in general, and simple anal ytical results are provided for the polariton problem. The method is t hen further utilized to consider exactly spatial dispersion in the ret arded photon Green's function.