Two anyons on the sphere: nonlinear states and spectrum
arXiv:1910.00587 · doi:10.1016/j.nuclphysb.2019.114906
Abstract
We study the energy spectrum of two anyons on the sphere in a constant magnetic field. Making use of rotational invariance we reduce the energy eigenvalue equation to a system of linear differential equations for functions of a single variable, a reduction analogous to separating center of mass and relative coordinates on the plane. We solve these equations by a generalization of the Frobenius method and derive numerical results for the energies of non-analytically derivable states.
32 pages, 2 figures