Calogero model with Yukawa like interaction

Kessabi, Mohammed; Saidi, El Hassan; Sebbata, Hanane

Calogero model with Yukawa like interaction

Authors

Kessabi, Mohammed

Saidi, El Hassan

Sebbata, Hanane

Description

We study an extension of one dimensional Calogero model involving strongly coupled and electrically charged particles. Besides Calogero term $\frac{g}{% 2x^{2}}$, there is an extra factor described by a Yukawa like coupling modeling short distance interactions. Mimicking Calogero analysis and using developments in formal series of the wave function $Ψ(x) $ factorised as $x^εΦ(x) $ with $ε(ε-1) =g$, we develop a technique to approach the spectrum of the generalized system and show that information on full spectrum is captured by $Φ(x) $ and $Φ^{\prime \prime}(x) $ at the singular point $x=0$ of the potential. Convergence of $% \int dx| Ψ(x) | ^{2}$ requires $ε>-{1/2}$ and is shown to be sensitive to the zero mode of $Φ(x) $ at $x=0$. \textbf{Key words}: \textit{Hamitonian systems, quantum integrability, Calogero model, Yukawa like potential.}
12 pages, 1 figure