Semiclassical path-integral quantization of nonintegrable Hamiltonian systems

Abstract

The periodic-orbit quantization approach of Gutzwiller, which is a semiclassical approximation of Feynman’s path-integral formalism, is used to calculate finite-resolution densities of states for a Hamiltonian system whose classical motion is dominated by chaos, viz., the hydrogen atom in a uniform magnetic field. In spectral regions where the resolution obtained is larger than the mean level spacing, it is possible to extract approximate eigenvalues of the quantized system. The particular role of stable periodic orbits and their direct quantization are elaborated. Remarkable agreement with exact quantum calculations results.