Classical Quantization of a Hamiltonian with Ergodic Behavior

摘要: Conservative Hamiltonian systems with two degrees of freedom are discussed where a typical trajectory fills the whole surface constant energy. The trace quantum mechanical Green's function is approximated by sum over classical periodic orbits. This leads directly to Selberg's formula for motion particle on negative curvature, and, when applied anisotropic Kepler problem, yields excellent results all energy levels.