Path Integral Approach for Quantum Motion on Spaces of Non-constant Curvature According to Koenigs

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dc.creatorGrosche, Christian
dc.date2006-08-29
dc.date.accessioned2026-07-07T07:26:32Z
dc.date.available2026-07-07T07:26:32Z
dc.descriptionIn this contribution I discuss a path integral approach for the quantum motion on two-dimensional spaces according to Koenigs, for short ``Koenigs-Spaces''. Their construction is simple: One takes a Hamiltonian from two-dimensional flat space and divides it by a two-dimensional superintegrable potential. These superintegrable potentials are the isotropic singular oscillator, the Holt-potential, and the Coulomb potential. In all cases a non-trivial space of non-constant curvature is generated. We can study free motion and the motion with an additional superintegrable potential. For possible bound-state solutions we find in all three cases an equation of eighth order in the energy E. The special cases of the Darboux spaces are easily recovered by choosing the parameters accordingly.
dc.identifierhttps://arxiv.org/abs/quant-ph/0608231
dc.identifierhttp://arxiv.org/abs/quant-ph/0608231
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/117113
dc.subjectQuantum Physics
dc.titlePath Integral Approach for Quantum Motion on Spaces of Non-constant Curvature According to Koenigs
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