A wave packet which travels on an elliptic trajectory is constructed for the hydrogen atom. This is achieved by mapping the Schrodinger equation for the hydrogen atom into the equation for a four-dimensional oscillator with a constraint. A set of coherent states for the constrained oscillator are then shown to have at high average energy the classical limit properties as obtained for planetary motion, to a good approximation.
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Bhaumik et al. (1986) studied this question.
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