Topological eigenfunctions of a trapped cold ion

Summary form only given. Theoretical studies of systems confined to one temporal and two spatial co-ordinates, reveal many novel quantum mechanical features. These features result from Lagrangians which exhibit topological (Chern-Simons) structures. It has been speculated that some of the more exotic features, such as the appearances of fermion-like properties, may have experimentally observable consequences in the behaviour of cooled atoms or ions. The motivation behind the present paper is to investigate this proposition further by determining the eigenfunction and eigenenergy spectrum of an ion moving in a constant magnetic field and an external trapping potential. Such an arrangement may be considered as the generic example of two-dimensional topological theory.