Fermion Ground State of Three Particles in a Harmonic Potential Well and Its Anyon Interpolation

TL;DR

This paper analyzes the exact analytic solution of three anyons in a harmonic potential, exploring its structure and interpolation to fermionic states, with focus on boundary conditions and mathematical properties.

Contribution

It provides a detailed analysis of the analytic structure of three-anyon solutions and their interpolation to fermion ground states in a harmonic potential.

Findings

Exact analytic solution for three anyons studied

Interpolation to fermion ground state demonstrated

Insights into boundary conditions and self-adjointness provided

Abstract

We examine the detail of the analytic structure of an exact analytic solution of three anyons, which interpolates to the fermion ground state in a harmonic potential well. The analysis is done on the fundamental domain with appropriate boundary conditions. Some remarks on the hard-core conditions and self-adjointness are made.