Information uncertainty-type inequalities in atomic systems

Guevara, Nicolais L.; Sagar, Robin P.; Esquivel, Rodolfo O.

doi:10.1063/1.1605932

Cited by 71 publications

(58 citation statements)

References 30 publications

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“…Fourth, in the present work we only calculate the Shannon entropy in position space, S r . In order to test the entropic uncertainty principle [45] for an atomic state in three-dimensional space, the Shannon entropy in corresponding momentum space, S p , should also be calculated, with…”

Section: Discussionmentioning

confidence: 99%

Shannon Information Entropy in Position Space for the Ground and Singly Excited States of Helium with Finite Confinements

2017

Atoms

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Abstract:We provide benchmark values for Shannon information entropies in position space for the ground state and ls2s 1 S e excited state of helium confined with finite confinement potentials by employing the highly correlated Hylleraas-type wave functions. For the excited state, a "tilt" (small oscillation) on the curve of Shannon entropy as a function of width size for the confinement potential is observed. Justified by the behavior of the electron density, the localization or delocalization of the helium wave functions confined with repulsive and attractive finite oscillator (FO) potentials are examined.

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Section: Discussionmentioning

confidence: 99%

Shannon Information Entropy in Position Space for the Ground and Singly Excited States of Helium with Finite Confinements

2017

Atoms

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“…We also discuss the Shannon entropies that are interpreted as localization measures of the distributions as a function of the interparticle and confining potentials. Shannon entropies at one-and two-particle levels have been discussed in the literature for models, atoms, and molecules, [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22]. We also analyze the Shannon entropy sums that are entropic formulations of the uncertainty principle [22,23].…”

Section: Introductionmentioning

confidence: 99%

Statistical correlations in the Moshinsky atom

Laguna

Sagar

2011

Phys. Rev. A

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We study the influence of the interparticle and confining potentials on statistical correlation via the correlation coefficient and mutual information in ground and some excited states of the Moshinsky atom in position and momentum space. The magnitude of the correlation between positions and between momenta is equal in the ground state. In excited states, the correlation between the momenta of the particles is greater than between their positions when they interact through an attractive potential whereas for repulsive interparticle potentials the opposite is true. Shannon entropies, and their sums (entropic formulations of the uncertainty principle), are also analyzed, showing that the one-particle entropy sum is dependent on the interparticle potential and thus able to detect the correlation between particles.

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“…This line of inquiry has recently led to numerous researchers to calculate the measures of information for various quantummechanical potentials of a specific analytic form [1][2][3][4][5][6][7][8][9] as well as for hydrogenic systems with standard and nonstandard dimensionalities [3,8,[10][11][12][13], circular membranes [14], confined systems [15,16], and many-electron systems [17][18][19][20][21].…”

Section: Introductionmentioning

confidence: 99%

Entropic functionals of Laguerre polynomials and complexity properties of the half‐line Coulomb potential

Sánchez-Moreno

Omiste

Dehesa

2011

Int J of Quantum Chemistry

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ABSTRACT:The stationary states of the half-line Coulomb potential are described by quantum-mechanical wavefunctions, which are controlled by the Laguerre polynomials L (1) n (x). Here, we first calculate the qth-order frequency or entropic moments of this quantum system, which is controlled by some entropic functionals of the Laguerre polynomials. These functionals are shown to be equal to a Lauricella function F, 1) by use of the Srivastava-Niukkanen linearization relation of Laguerre polynomials. The resulting general expressions are applied to obtain the following information-theoretic quantities of the half-line Coulomb potential: disequilibrium, Renyi and Tsallis entropies. An alternative and simpler expression for the linear entropy is also found by means of a different method. Then, the Shannon entropy and the LMC shape complexity of the lowest and highest (Rydberg) energetic states are explicitly given; moreover, sharp information-theoretic-based upper bounds to these quantities are found for general physical states. These quantities are numerically discussed for the ground and various excited states. Finally, the uncertainty measures of the half-line Coulomb potential given by the information-theoretic lengths are discussed.

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Information uncertainty-type inequalities in atomic systems

Cited by 71 publications

References 30 publications

Shannon Information Entropy in Position Space for the Ground and Singly Excited States of Helium with Finite Confinements

Shannon Information Entropy in Position Space for the Ground and Singly Excited States of Helium with Finite Confinements

Statistical correlations in the Moshinsky atom

Entropic functionals of Laguerre polynomials and complexity properties of the half‐line Coulomb potential

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