Quantum information entropies for position-dependent mass Schrödinger problem

G. Yañez-Navarro, Guo Hua Sun, T. Dytrych, K. D. Launey, Shi Hai Dong, J. P. Draayer

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Abstract

The Shannon entropy for the position-dependent Schrödinger equation for a particle with a nonuniform solitonic mass density is evaluated in the case of a trivial null potential. The position S x and momentum S p information entropies for the three lowest-lying states are calculated. In particular, for these states, we are able to derive analytical solutions for the S x entropy as well as for the Fourier transformed wave functions, while the S p quantity is calculated numerically. We notice the behavior of the S x entropy, namely, it decreases as the mass barrier width narrows and becomes negative beyond a particular width. The negative Shannon entropy exists for the probability densities that are highly localized. The mass barrier determines the stability of the system. The dependence of S p on the width is contrary to the one for S x. Some interesting features of the information entropy densities ρs (x) and ρs (p) are demonstrated. In addition, the Bialynicki-Birula-Mycielski (BBM) inequality is tested for a number of states and found to hold for all the cases. © 2014 Elsevier Inc.
Original languageAmerican English
Pages (from-to)153-160
Number of pages136
JournalAnnals of Physics
DOIs
StatePublished - 1 Jan 2014

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Yañez-Navarro, G. ; Sun, Guo Hua ; Dytrych, T. ; Launey, K. D. ; Dong, Shi Hai ; Draayer, J. P. / Quantum information entropies for position-dependent mass Schrödinger problem. In: Annals of Physics. 2014 ; pp. 153-160.
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abstract = "The Shannon entropy for the position-dependent Schr{\"o}dinger equation for a particle with a nonuniform solitonic mass density is evaluated in the case of a trivial null potential. The position S x and momentum S p information entropies for the three lowest-lying states are calculated. In particular, for these states, we are able to derive analytical solutions for the S x entropy as well as for the Fourier transformed wave functions, while the S p quantity is calculated numerically. We notice the behavior of the S x entropy, namely, it decreases as the mass barrier width narrows and becomes negative beyond a particular width. The negative Shannon entropy exists for the probability densities that are highly localized. The mass barrier determines the stability of the system. The dependence of S p on the width is contrary to the one for S x. Some interesting features of the information entropy densities ρs (x) and ρs (p) are demonstrated. In addition, the Bialynicki-Birula-Mycielski (BBM) inequality is tested for a number of states and found to hold for all the cases. {\circledC} 2014 Elsevier Inc.",
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Quantum information entropies for position-dependent mass Schrödinger problem. / Yañez-Navarro, G.; Sun, Guo Hua; Dytrych, T.; Launey, K. D.; Dong, Shi Hai; Draayer, J. P.

In: Annals of Physics, 01.01.2014, p. 153-160.

Research output: Contribution to journalArticleResearchpeer-review

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