Monotonicity in confined system problems

摘要

When an atom is confined at the center of a spherically symmetric impenetrable sphere, the electron density is altered. Of particular interest are the changes in the electron density at the center of the cavity as they affect important physical properties such as the isotropic constants of the hyperfine structure. This work presents four simple theorems that facilitate understanding the behavior of the electron density of the ground state with variations in the potential or in the radius of the impenetrable spherical cavity. The general statements are illustrated by discussion of the known results for confined and free systems and the results of simple evaluations for model hydrogen-like atoms in a cavity.