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Title: Statistical correlations in the Moshinsky atom

Abstract

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.

Authors:
;  [1]
  1. Departamento de Quimica, Universidad Autonoma Metropolitana San Rafael Atlixco No. 186, Iztapalapa, 09340 Mexico Distrito Federal (Mexico)
Publication Date:
OSTI Identifier:
22051290
Resource Type:
Journal Article
Journal Name:
Physical Review. A
Additional Journal Information:
Journal Volume: 84; Journal Issue: 1; Other Information: (c) 2011 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1050-2947
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 74 ATOMIC AND MOLECULAR PHYSICS; ENTROPY; EXCITED STATES; GROUND STATES; POTENTIALS; STATISTICAL MODELS; UNCERTAINTY PRINCIPLE

Citation Formats

Laguna, H G, and Sagar, R P. Statistical correlations in the Moshinsky atom. United States: N. p., 2011. Web. doi:10.1103/PHYSREVA.84.012502.
Laguna, H G, & Sagar, R P. Statistical correlations in the Moshinsky atom. United States. https://doi.org/10.1103/PHYSREVA.84.012502
Laguna, H G, and Sagar, R P. 2011. "Statistical correlations in the Moshinsky atom". United States. https://doi.org/10.1103/PHYSREVA.84.012502.
@article{osti_22051290,
title = {Statistical correlations in the Moshinsky atom},
author = {Laguna, H G and Sagar, R P},
abstractNote = {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.},
doi = {10.1103/PHYSREVA.84.012502},
url = {https://www.osti.gov/biblio/22051290}, journal = {Physical Review. A},
issn = {1050-2947},
number = 1,
volume = 84,
place = {United States},
year = {Fri Jul 15 00:00:00 EDT 2011},
month = {Fri Jul 15 00:00:00 EDT 2011}
}