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Shannon entropy and Fisher information of the one-dimensional Klein–Gordon oscillator with energy-dependent potential

Abdelmalek Boumali

Laboratoire de Physique Appliquée et Théorique, Université Larbi-Tébessi-Tébessa, Algeria

E-mail Address: boumali.abdelmalek@gmail.com

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and

Malika Labidi

Laboratoire de Physique Appliquée et Théorique, Université Larbi-Tébessi-Tébessa, Algeria

E-mail Address: labidimalika89@gmail.com

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https://doi.org/10.1142/S0217732318500335Cited by:23 (Source: Crossref)

Abstract

In this paper, we studied, at first, the influence of the energy-dependent potentials on the one-dimensionless Klein–Gordon oscillator. Then, the Shannon entropy and Fisher information of this system are investigated. The position and momentum information entropies for the low-lying states n = 0, 1, 2 are calculated. Some interesting features of both Fisher and Shannon densities, as well as the probability densities, are demonstrated. Finally, the Stam, Cramer–Rao and Bialynicki–Birula–Mycielski (BBM) inequalities have been checked, and their comparison with the regarding results have been reported. We showed that the BBM inequality is still valid in the form $S_{x} + S_{p} \geq 1 + ln π$ $S_{x} + S_{p} \geq 1 + ln π$ , as well as in ordinary quantum mechanics.

Keywords:

PACS: 03.65.Aa, 03.65.Ge, 03.65.Pm

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