Abstract
We revisit the Anisotropic Kepler Problem (AKP), which concerns with trajectories of an electron with anisotropic mass term in a Coulomb field. This is one of the most fundamental fields in Quantum Chaos. Nowadays various quantum systems are challenging us. Classical theories of these may have chaos. Quantum mechanics have developed from integrable cases and may have to be reformulated for such cases. AKP then serves as a suitable testing ground for quantum chaos. We first review a pioneering work by Martin Gutzwiller (J Math Phys (1977) 18:106). We shall show the systematics of the trajectories using ample figures from an extensive numerical analysis. Then we focus on the role of hyperbolic singularities and we comment on the approximations in an analytic formulation.
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