Dynamics of States with Non-Zero Moment in Own Field

Abstract

The paper studies a nonstationary self-consistent quantum system that intensively interacts with its own field. At a non-zero moment, the psi function cannot be independent of the angles of the spherical coordinate system. In this paper, a superposition of angular distributions is found, leading to a spherically symmetric charge distribution for the whole value of the moment (l=1).The paper defines the conditions under which in the case of half-integer values of the moment  the charge density distribution turns out to be spherically symmetric. In this case, a self-consistent system can be described by a system of ordinary differential equations. In the final section, a classical collisionless one-component system of charged particles characterized by a nonzero moment is considered.