Distributed Charge in a Coulomb Potential Well

Abstract

The behavior of a distributed charge in a Coulomb potential well is considered. It is shown that elements of a distributed charge can move along different trajectories, thus forming actually motion of a charge wave. Propagation over different trajectories is possible because elements of charge have on these trajectories the same energy. The overall velocity of motion of a charge wave is one half the velocity of individual elements in the wave, and the wave can move only along the $\varphi$ axis of a spherical coordinate system. The following features in the motion of a distributed charge are stressed: each point of the charge is a center from which elements of the charge propagate with the same velocity within the solid angle $2\pi$. The set of spherical functions needed to describe a distributed charge is specified, and it is shown that a charge cannot have spherical symmetry.