Dynamics of Charged Spherical Clusters in a Self-consistent Field

Abstract

This study investigates non-stationary self-consistent single-component charge systems that interact intensively with their field. Classical collisionless systems are considered, which are described by a kinetic equation utilising motion integrals that remain valid in the absence of stationarity. The concept of the "Meshchersky integral" is introduced, used alongside the Kapchinsky integral. Furthermore, several quantum mechanical systems are examined. In this case, the study reduces to solving complex non-stationary Schrödinger equations. Only when the orbital angular momentum is zero does the studied system exhibit spherical symmetry. The conditions are identified under which the charge density remains spherically symmetric even when the angular momentum is nonzero. States with half-integer angular momentum present particular complexity. The psi-function has a spinorial nature. Solutions are found where the charge density remains spherically symmetric.