Wave-packet solutions of the Schr\"odinger equation for the Coulomb potential are obtained that travel along classical elliptic orbits of fixed mean eccentricity and angular momentum. These wave packets are coherent states that have minimal quantum fluctuations in the noncommuting components of the Lenz vector in the plane of the orbit. For large quantum numbers the asymptotic form of the wave packet and the classical equations of the orbit are obtained analytically.
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Michael Nauenberg (1989) studied this question.
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