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Physics Letters A

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

S. H. Patil, K. D. Sen

Published Jun 4, 2007• 16 citations
Publisher
DOI
10.1016/j.physleta.2007.05.085

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Abstract The dimensional analyses of the position and momentum variances‐based 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, −Z(e−μr/r), and (ii) Hulthén‐like, −Zμ(1/(eμr − 1)), potentials by cos(bμr) followed by addition of the term a/r2, where a and b ≥ 0, μ 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 [μ, Z] at a fixed value of μ/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. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2007

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Characteristic features of net information measures for constrained Coulomb potentials

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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 , 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.

Journal of Physics B Atomic Molecular and Optical Physics•May 24, 2007•45 citations
Abstract The dimensional analyses of the position and momentum variances‐based 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, −Z(e−μr/r), and (ii) Hulthén‐like, −Zμ(1/(eμr − 1)), potentials by cos(bμr) followed by addition of the term a/r2, where a and b ≥ 0, μ 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 [μ, Z] at a fixed value of μ/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. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2007
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 , 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.