We study two interacting electrons confined within a quantum ring. For a narrow-width ring the radial motion is the fastest one and adiabatically decoupled from the angular motions. The role of the Coulomb interaction and the confining potential is to build a rotating Wigner molecule with the relative angular motion in form of harmonic oscillations. We calculate the electronic states and discuss the thermodynamical properties of two-electron quantum rings. It is shown that a strong correlation exists between the quantum numbers of rotation and oscillation of the Wigner molecule.
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Wendler et al. (1996) studied this question.