Asymptotic analysis and spectrum of three anyons

The spectrum of anyons confined in a harmonic oscillator potential shows both linear and nonlinear dependence on the statistical parameter. While the existence of exact linear solutions has been shown analytically, the nonlinear dependence has been arrived at by numerical and/or perturbative methods. We develop a method which shows the possibility of a nonlinearly interpolating spectrum. To be specific we analyze the eigenvalue equation in various asymptotic regions for the three-anyon problem