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Open Quantum Systems Decoherence Quantum Simulation

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

arXiv

Authors: Christian Grosche

Year

2007

Paper ID

49290

Status

Preprint

Abstract Read

~2 min

Abstract Words

106

Citations

N/A

Abstract

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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In this contribution a path integral approach for the quantum motion on three-dimensional spaces according to Koenigs, for short"Koenigs-Spaces", is discussed.

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References & Citation Signals

[1] DOI https://doi.org/arXiv:0708.3082 [2] arXiv https://arxiv.org/abs/0708.3082 [3] Publisher https://arxiv.org/abs/0708.3082

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