Two electronic states in a quantum ring: Mathieu equation approach

The problem of two-electronic states is considered for the case of thin GaAs quantum ring in the framework of adiabatic approximation. It is assumed that electrons are localized on a circle, and the Coulomb interaction between the electrons depends only on angular coordinates. The real Coulomb interaction is replaced by function which makes it possible the separation of relative motion and the motion of the center of mass. The Mathieu equation is obtained for the relative motion of electrons. The harmonic, anharmonic and the libration regimes of oscillations are discussed.