Path integral treatment of a noncentral electric potential

• Authors: Ali Ghoumaid , Farid Benamira , Larbi Guechi , Zohra Khiat
• Languages of publication: EN

Abstracts

EN

We present a rigorous path integral treatment of a dynamical system in the axially symmetric potential
$V(r,\theta ) = V(r) + \tfrac{1}
{{r^2 }}V(\theta )
$
. It is shown that the Green’s function can be calculated in spherical coordinate system for
$V(\theta ) = \frac{{\hbar ^2 }}
{{2\mu }}\frac{{\gamma + \beta \sin ^2 \theta + \alpha \sin ^4 \theta }}
{{\sin ^2 \theta \cos ^2 \theta }}
$
. As an illustration, we have chosen the example of a spherical harmonic oscillator and also the Coulomb potential for the radial dependence of this noncentral potential. The ring-shaped oscillator and the Hartmann ring-shaped potential are considered as particular cases. When α = β = γ = 0, the discrete energy spectrum, the normalized wave function of the spherical oscillator and the Coulomb potential of a hydrogen-like ion, for a state of orbital quantum number l ≥ 0, are recovered.

Keywords

EN

noncentral potential; Coulomb potential; harmonic oscillator; Pöschl-Teller potential; Green’s function; path integral; bound states

• Publisher: De Gruyter Open
• Journal: Open Physics
• Year: 2013
• Volume: 11
• Issue: 1
• Pages: 78-88

Dates

published

1 - 1 - 2013

online

15 - 1 - 2013

Contributors

author

Ali Ghoumaid

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

author

Farid Benamira

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

author

Larbi Guechi

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

author

Zohra Khiat

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

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Identifiers

DOI

10.2478/s11534-012-0125-9