Entropic system in the relativistic Klein-Gordon Particle

C A Onate,M C Onyeaju

doi:10.46481/jnsps.2021.209

Abstract

The solutions of Kratzer potential plus Hellmann potential was obtained under the Klein-Gordon equation via the parametric Nikiforov-Uvarov method. The relativistic energy and its corresponding normalized wave functions were fully calculated. The theoretic quantities in terms of the entropic system under the relativistic Klein-Gordon equation (a spinless particle) for a Kratzer-Hellmann’s potential model were studied. The effects of a and b respectively (the parameters in the potential that determine the strength of the potential) on each of the entropy were fully examined. The maximum point of stability of a system under the three entropies was determined at the point of intersection between two formulated expressions plotted against a as one of the parameters in the potential. Finally, the popular Shannon entropy uncertainty relation known as Bialynick-Birula, Mycielski inequality was deduced by generating numerical results.

Highlights

The understanding of correlations in quantum systems is based on the analytic tools provided by the entropic measures
Shannon entropy has been widely reported under the non-relativistic wave equation over the years for different potential models [2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25]
The accuracy of Shannon entropy for any calculation can be checked by the uncertainty relation of Shannon entropy that relates position space and momentum space with the spatial dimension

Summary

Introduction

The understanding of correlations in quantum systems is based on the analytic tools provided by the entropic measures. Shannon entropy has been widely reported under the non-relativistic wave equation over the years for different potential models [2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25]. The authors want to examine the entropic system under the relativistic Klein-Gordon equation using Kratzer-Hellmann potential. The physical form of Kratzer-Hellmann potential is where pis the momentum operator, M is the particle’s mass, E is the relativistic energy and R(r) is the wave function. When invoked on equation (23), using an appropriate integral, we have the normalization factor as

Kratzer-Hellmann potential and entropies

Tsallis entropy

Results and Discussion

Conclusions