Abstract

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 [1]. 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. The calculations clarify and enhance previous work [1], [2].

© 2000 IEEE