1998/08/27 by Christian Grosche
Physics and Astronomy · #quant-ph
published as Int.J.Theor.Phys. 38 (1999) 955-969 · LaTeX 12 pp., one figure
arxiv created 1998/08/27 · arxiv updated 2009/12/01
In this paper I discuss by means of path integrals the quantum dynamics of a charged particle on the hyperbolic plane under the influence of an Aharonov-Bohm gauge field. The path integral can be solved in terms of an expansion of the homotopy classes of paths. I discuss the interference pattern of scattering by an Aharonov-Bohm gauge field in the flat space limit, yielding a characteristic oscillating behavior in terms of the field strength. In addition, the cases of the isotropic Higgs-oscillator and the Kepler-Coulomb potential on the hyperbolic plane are shortly sketched.