Broken symmetry of the charged planar rotator in electric and magnetic fields

Abstract

An exact solution to the problem of the Stark and Zeeman effects of the charged two-dimensional rotator is given. The energy spectrum is shown to exhibit an unusual degeneracy-breaking pattern. Group theory is used to account for the contrasting symmetry properties of the electric and magnetic field solutions. An examination of the physical properties of the system by means of perturbation theory leads to a clarification of an important point concerning the use of degenerate perturbation theory and the analytical continuity of perturbation wave functions.