Scaling properties of net information measures for superpositions of power potentials: free and spherically confined cases

Abstract

The dimensional analyses of the position and momentum variances based quantum mechanical Heisenberg uncertainty measure, along with several entropic information measures are carried out for the superposition of the power potentials of the form V(r)=Zrⁿ+Σ_iZ_ir^n_i where Z, Z_i, n, n_i are parameters yielding bound states for a particle of mass M. The uncertainty product and all other net information measures for given values of the parameters Z, Z_i, are shown to depend only on M and the ratios Z_i/Z(^n_i+2)/(n+2). Under the imposition of a spherical impenetrable boundary of radius R over the polynomial potential, an additional parametric dependence on RZ^1/(n+2) is derived. A representative set of numerical results are presented which support the validity of such a general scaling property.