Studies of Bogomolny's semiclassical quantization of integrable and nonintegrable systems

The semiclassical quantization scheme formulated by Bogomolny, employing a suitably chosen Poincare surface of section (PSS), has been used to calculate approximate energy eigenvalues for the quantum analogues of several Hamiltonian systems. Using a finite approximation to the transfer operator in coordinate space, we have carried out calculations of the energy eigenvalues for the circle billiard and the 45 degrees wedge billiard, both of which …