QUANTIZATION OF SINAIS BILLIARD - A SCATTERING APPROACH

We obtained the spectrum of the Sinai billiard as the zeros of a secul ar equation, which is based on the scattering matrix of a related scat tering problem. We show that this quantization method provides an effi cient numerical scheme, and its implementation for the present case gi ves a few thousands of levels without encountering any serious difficu lty. We use the numerical data to check some approximations which are essential for the derivation of a semiclassical quantization method ba sed also on this scattering approach.