The elliptic eigenstates of the hydrogen atom are the quantum analogs of the classical trajectories of the electron around the nucleus in the sense that they have the best transverse localization compatible with the uncertainty relations. The equivalence of the hydrogen atom with a harmonic oscillator provides us with a realization of the symmetry group and allows for the analytical study of the elliptic states. In particular we derive the 2D and 3D wave functions in a simple closed form.
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Léna et al. (1991) studied this question.
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