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

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

2006-08-29

arxiv.org/abs/quant-ph/0608231v1

Physics

Quantum Physics

Scientific paper

In 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.

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