Quantization of Sinai's Billiard - A Scattering Approach

We obtained the spectrum of the Sinai billiard as the zeroes of a secular equation, which is based on the scattering matrix of a related scattering problem. We show that this quantization method provides an efficient numerical scheme, and its implementation for the present case gives a few thousands of levels without encountering any serious difficulty. We use the numerical data to check some approximations which are essential for the derivation of a semiclassical quantization method based also on this scattering approach.