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

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dc.creatorGrosche, Christian
dc.date2007-08-22
dc.date.accessioned2026-07-07T08:25:07Z
dc.date.available2026-07-07T08:25:07Z
dc.descriptionIn this contribution a path integral approach for the quantum motion on three-dimensional spaces according to Koenigs, for short``Koenigs-Spaces'', is discussed. Their construction is simple: One takes a Hamiltonian from three-dimensional flat space and divides it by a three-dimensional superintegrable potential. Such superintegrable potentials will be the isotropic singular oscillator, the Holt-potential, the Coulomb potential, or two centrifugal potentials, respectively. In all cases a non-trivial space of non-constant curvature is generated. In order to obtain a proper quantum theory a curvature term has to be incorporated into the quantum Hamiltonian. For possible bound-state solutions we find equations up to twelfth order in the energy E.
dc.description20 pages, 1 figure
dc.identifierhttps://arxiv.org/abs/0708.3082
dc.identifierhttp://arxiv.org/abs/0708.3082
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/136560
dc.subjectQuantum Physics
dc.titlePath Integral Approach for for Quantum Motion on Spaces of Non-constant Curvature According to Koenigs: Three Dimensions
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