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Shannon information entropy in the presence of magnetic and Aharanov–Bohm (AB) fields

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Abstract

In this research article, quantum information-theoretic analysis of the class of Yukawa potential (CYP) has been considered in the presence of magnetic and Aharanov–Bohm (AB) fields both analytically. We solve the Schrodinger equation in the presence of external magnetic and AB fields for the CYP via the functional analysis approach to obtain the energy equation and wave function, respectively. The probability density is then obtained by squaring the wave function which is then used to obtain the Shannon entropy numerically. From our results, we note that the all-inclusive effect of the magnetic and AB fields influences the Shannon entropies such that negative values are observed, demonstrating that negative entropies exist which physically means that the probability densities are highly localized in this region. The variation in the Shannon entropy with the screening parameter \(\alpha\), magnetic and AB fields for the CYP is discussed. The Bialynicki-Birula, Mycielski inequality (BBM) uncertainty relation is also verified. The content of this research finds application in atomic and molecular physics, quantum chemistry and physics.

Graphic abstract

In this study, Shannon information entropy is investigated with the class of Yukawa potential in position and momentum spaces in the presence of magnetic and Aharanov–Bohm (AB) fields. The all-inclusive effect of the magnetic and AB fields influences the Shannon entropies such that negative values are observed, which physically means that the probability densities are highly localized in this region. The Shannon entropy measure satisfied the Bialynicki-Birula and Mycielski (BBM) uncertainty.

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Acknowledgements

The authors dedicate this work to Late Professor Eno Ekpo Eno. We also thank the anonymous referees for the careful reading and the suggestions that improved the paper.

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  1. Theoretical Physics Group, Department of Physics, University of Port Harcourt, Choba, Nigeria

    C. O. Edet & A. N. Ikot

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  1. C. O. Edet
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Edet, C.O., Ikot, A.N. Shannon information entropy in the presence of magnetic and Aharanov–Bohm (AB) fields. Eur. Phys. J. Plus 136, 432 (2021). https://doi.org/10.1140/epjp/s13360-021-01438-4

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