Path Integral Solution for the Coulomb Potential in a Curved Space of Constant Positive Curvature |
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Authors: | L. Aggoun N. Bounouioua F. Benamira L. Guechi |
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Affiliation: | 1.Laboratoire de Physique Théorique, Département de Physique, Faculté des Sciences Exactes,Université des Frères Mentouri,Constantine,Algeria |
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Abstract: | A new path integral treatment of a hydrogen-like atom in a uniformly curved space with a constant positive curvature is presented. By converting the radial path integral into a path integral for the modified Pöschl-Teller potential with the help of the space-time transformation technique, the radial Green’s function is expressed in closed form, from which the energy spectrum and the corresponding normalized wave functions of the bound states are extracted. In the limit of vanishing curvature, the Green’s function, the energy spectra and the correctly normalized wave functions of bound and scattering states for a standard hydrogen-like atom are found. |
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