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Bound States for a Klein–Gordon Particle in Vector Plus Scalar Generalized Hulthén Potentials in D Dimensions

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Abstract

The Green’s function associated with a Klein–Gordon particle moving in a D-dimensional space under the action of vector plus scalar q-deformed Hulthén potentials is constructed by path integration for \({q \geq 1}\) and \({\frac{1}{\alpha} \ln q < r < \infty}\). An appropriate approximation of the centrifugal potential term and the technique of space-time transformation are used to reduce the path integral for the generalized Hulthén potentials into a path integral for q-deformed Rosen–Morse potential. Explicit path integration leads to the radial Green’s function for any l state in closed form. The energy spectrum and the correctly normalized wave functions, for a state of orbital quantum number \({l \geq 0}\), are obtained. Eventually, the vector q-deformed Hulthén potential and the Coulomb potentials in D dimensions are considered as special cases.

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Authors and Affiliations

  1. Laboratoire de Physique Théorique, Département de Physique, Faculté des Sciences Exactes, Université des frères Mentouri, Route d’Ain El Bey, Constantine, Algeria

    L. Aggoun, F. Benamira, L. Guechi & M. A. Sadoun

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  1. L. Aggoun
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  2. F. Benamira
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  3. L. Guechi
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  4. M. A. Sadoun
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Correspondence to L. Guechi.

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Aggoun, L., Benamira, F., Guechi, L. et al. Bound States for a Klein–Gordon Particle in Vector Plus Scalar Generalized Hulthén Potentials in D Dimensions. Few-Body Syst 57, 229–239 (2016). https://doi.org/10.1007/s00601-015-1037-1

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  • DOI: https://doi.org/10.1007/s00601-015-1037-1

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