Net information measures for modified Yukawa and Hulthén potentials

Abstract

ABSTRACT:The dimensional analyses of the position and momentum variancesbased quantum mechanical Heisenberg uncertainty measure, as well as the entropic information measures given by the Shannon information entropy sum and the product of Fisher information measures are carried out for two widely used nonrelativistic isotropic exponential-cosine screened Coulomb potentials generated by multiplying the superpositions of (i) Yukawa-like, Ϫ Z ͑e Ϫr /r), and (ii) Hulthén-like, Ϫ Z ͑1/͑e r Ϫ 1͒͒, potentials by cos(br) followed by addition of the term a/r 2 , where a and b Ն 0, are the screening parameters and Z, in case of atoms, denotes the nuclear charge. Under the spherical symmetry, all the information measures considered are shown to be independent of the scaling of the set [, Z] at a fixed value of /Z, a, and b and the other parameters defining the superpositions of the potentials. Numerical results are presented, which support the validity of the scaling properties.

Shannon information entropy for an infinite circular well

“…Except for their own significance in physics, the BBM relations have been used widely in atomic and molecular physics [6][7][8][9][10]. For example, the Shannon information entropies for a few molecular potentials have been analytically obtained [11][12][13][14][15][16][17][18][19][20], i.e., the harmonic oscillator [1,11], the Pöschl-Teller (PT) [12,13], the Morse [12,14], the Coulomb [15], the potential isospectral to the PT potential [16], the classical orthogonal polynomials [17] and other studies [18][19][20]. This stimulates us to solve those untouched but interesting quantum systems due to their applications in physics.…”

Quantum information‐theoretic measures for the static screened Coulomb potential

“…They are widely used in quantum physics in the analysis of quantum entanglement, quantum revivals, atomic ionization properties . Other several investigations have been carried out for different quantum mechanical systems …”

Position and momentum information‐theoretic measures of the pseudoharmonic potential

“…The information‐theoretic quantities have also been discussed using scaling properties of the systems . The relativistic effect have also been considered in the study of the information‐theoretic quantities .…”