A class of exact solutions for N anyons in a N-body potential

Abstract

A class of exact solutions are obtained for the problem of N anyons interacting via the N-body potential V(x₁, x₂,.., x_N) = -e²/[(1/N) ∑_i<j(x_i - x_j)²]^½. Unlike the oscillator case the resulting spectrum is not linear in the anyon parameter α (0 ≤ α ≤ 1). However, as in the oscillator case, crossover between the ground states is shown to occur for N anyons (N ≥ 3) experiencing the above potential.