A SCATTERING APPROACH TO THE QUANTIZATION OF HAMILTONIANS IN 2-DIMENSIONS - APPLICATION TO THE WEDGE BILLIARD

We extend the scattering approach to quantize general Hamiltonian syst ems in two dimensions and demonstrate it for the wedge billiard. The r esulting energy levels are given by the zeros of a secular equation. T he corresponding wavefunctions may also be constructed. We verify anal ytically that this quantization condition is exact in the case of the integrable wedges. This method has been applied successfully to comput ing numerically a few thousand levels for various values of the angle. Using these data, we can check the Gutzwiller trace formula and other semiclassical relations involving the scattering matrix and periodic orbits, for which we find excellent agreement.