Characteristic features of net information measures for constrained Coulomb potentials

Abstract

The dimensional analyses of the position and momentum variance based quantum mechanical Heisenberg uncertainty measure and the other useful net entropic information measures for the bound states of two constrained Coulomb potentials are reported for the first time. The potentials describe an electron moving in the central field due to a nucleus of charge Z with radius R defining the constraints as (a) the truncated potential given by −Z/(rⁿ+Rⁿ)^1/n, and (b) the radius of the impenetrable spherical wall. The net information measures for the two potentials are explicitly shown to be independent of the scaling of the set [Z, R] at a fixed value of ZR. Analytic proof is presented, for the first time, showing the presence of a characteristic extremum in the variation of the net information entropy as a function of the radius R with its location scaling as Z⁻¹. Numerical results are presented which support the validity of the scaling properties.