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

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

2007-08-22

arxiv.org/abs/0708.3082v1

Physics

Quantum Physics

20 pages, 1 figure

Scientific paper

In 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.

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