Eur. Phys. J. D 41, 397-402 (2007)
https://doi.org/10.1140/epjd/e2006-00221-1

Two-particle Wigner functions in a one-dimensional Calogero-Sutherland potential

Department of Physics, Faculty of Sciences, Ankara University, 06100 Tandoğan, Ankara, Turkey

Corresponding author: ^a tegmen@science.ankara.edu.tr

Received: 12 April 2006
Revised: 4 September 2006
Published online: 29 September 2006

Abstract

We calculate the Wigner distribution function for the Calogero-Sutherland system which consists of harmonic and inverse-square interactions. The Wigner distribution function is separated out into two parts corresponding to the relative and center-of-mass motions. A general expression for the relative Wigner function is obtained in terms of the Laguerre polynomials by introducing a new identity between Hermite and Laguerre polynomials.