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The Solutions on One-Dimensional Dirac Oscillator with Energy-Dependent Potentials and Their Effects on the Shannon and Fisher Quantities of Quantum Information Theory

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Abstract

In this paper, we focus, at first, on the exact solutions on the one-dimensional Dirac oscillator with the energy-dependent potentials. Then, the influence of these solutions on the Shannon entropy and Fisher information, well-known in quantum information, has been studied. In this direction, we concentrated on the determination of the position and momentum information entropies for the low-lying states n=0,1,2. Some interesting features of both Fisher and Shannon densities as well as the probability densities are demonstrated. Finally, the Fisher uncertainty relation, 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 \(S_{x}+S_{p}\ge 1+\text {ln}\pi \).

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Acknowledgements

The authors would like to thank Prof Lyazid Chetouani, University of Constantine, Algeria, for his personal communication about the modified product scalar in the Dirac equation. This work was fully supported by the ‘’ Direction Générale de la Recherche Scientifique et du Développement Technologique (DGRSDT)’’ of Algeria.

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

    Abdelmalek Boumali & Malika Labidi

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  1. Abdelmalek Boumali
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  2. Malika Labidi
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Correspondence to Abdelmalek Boumali.

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Boumali, A., Labidi, M. The Solutions on One-Dimensional Dirac Oscillator with Energy-Dependent Potentials and Their Effects on the Shannon and Fisher Quantities of Quantum Information Theory. J Low Temp Phys 204, 24–47 (2021). https://doi.org/10.1007/s10909-021-02596-6

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