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For homogeneous potentials, the sum S(T), of position and momentum Shannon information entropies Sr and Sp is shown to be independent of the coupling strength scaling. The other commonly used uncertainty like products also follow similar behavior. The ramifications of this scaling property in the cases of hydrogenlike, harmonic oscillator, Morse, and(More)
The Shannon information entropy of 1-normalized electron density in position and momentum space Sr and Sp, and the sum ST, respectively, are reported for the ground-state H, He+, Li2+, H-, He, Li+, Li, and B atoms confined inside an impenetrable spherical boundary defined by radius R. We find new characteristic features in ST denoted by well-defined minimum(More)
The net Fisher information measure IT , defined as the product of position and momentum Fisher information measures Ir and Ik and derived from the non-relativistic Hartree-Fock wave functions for atoms with Z = 1−102, is found to correlate well with the inverse of the experimental ionization potential. Strong direct correlations of IT are also reported for(More)
In proof theory we use category theory to obtain identity criteria for deductions. Inference rules, by which we pass from one deduction to another, correspond there to partial algebraic operations. This is an algebra built on deductions and not on formulae. Logic is thereby tied to algebras of another kind than Boolean algebras, Heyting algebras, and(More)
The Lagrange-mesh method is an approximate variational calculation which resembles a mesh calculation because of the use of a Gauss quadrature. The hydrogen atom confined in a sphere is studied with Lagrange-Legendre basis functions vanishing at the center and surface of the sphere. For various confinement radii, accurate energies and mean radii are(More)
The central role of the shape function sigma(r) from the density functional theory (DFT), the ratio of the electron density rho(r) and the number of electrons N of the system (density per particle), is investigated. Moreover, its relationship with DFT based reactivity indices is established. In the first part, it is shown that an estimate for the chemical(More)
Information-theoretic measures are employed to describe the course of a three-center chemical reaction in terms of detecting the transition state and the stationary points unfolding the bond-forming and bond-breaking regions which are not revealed in the energy profile. The information entropy profiles for the selected reactions are generated by following(More)
Calculations of electronic energy and static dipole polarizability are reported for the hydrogen atom in the ns states (n = 1-6) confined between two impenetrable concentric spheres of inner and outer radii placed at the locations of the radial nodes corresponding to the free hydrogen ns (n = 2-7) orbitals. Interesting new conditions of degeneracy arising(More)
Abstract Position and momentum information measures are evaluated for the ground state of the relativistic hydrogen-like atoms. Consequences of the fact that the radial momentum operator is not self-adjoint are explicitly studied, exhibiting fundamental shortcomings of the conventional uncertainty measures in terms of the radial position and momentum(More)
Lower bound for the shape complexity measure of López-Ruiz-Mancini-Calbet (LMC), C LM C , is derived. Analytical relations for simple examples of the harmonic oscillator, the hydrogen atom and two-electron 'entangled artificial' atom proposed by Moshinsky are derived. Several numerical examples of the spherically confined model systems are presented as the(More)