Mapping the Calogero model on the Anyon model

We explicitly map the N-body one dimensional Calogero eigenstates in a harmonic well to the lowest Landau level sector of N-body eigenstates of the two dimensional anyon model in a harmonic well. The mapping is achieved in terms of a convolution kernel that uses as input the scattering eigenstates of the free Calogero model on the infinite line, which are obtained in an operator formulation.