Calogero model with Yukawa-like interaction
Abstract We study an extension of one-dimensional Calogero model involving strongly coupled and electrically charged particles. Besides Calogero term g 2 x 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 ) factorized as x ɛ Φ ( x ) with ɛ ( ɛ − 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 ″ ( x ) at the singular point x = 0 of the potential. Convergence of ∫ d x | Ψ ( x ) | 2 requires ɛ > − 1 2 and is shown to be sensitive to the zero mode of Φ ( x ) at x = 0 .