Information-theoretic measure of the hyperbolical exponential-type potential

Atachegbe Clement Onate,Olukayode Adebimpe,Adewale Folaranmi Lukman,Babatunde Olufemi Adebesin

doi:10.3906/fiz-1802-40

Abstract

The approximate analytical solution of the 3-dimensional radial Schrödinger equation in the framework of the parametric Nikiforov-Uvarov method was obtained with a hyperbolical exponential-type potential. The energy eigenvalue equation and the corresponding wave function have been obtained explicitly. Using the integral method, we calculated Shannon entropy, information energy, Fisher information, and complexity measure. It was deduced that the complexity measure calculated using Shannon entropy with information energy and that calculated using Shannon entropy with Fisher information were similar.

Highlights

In recent years, various quantum mechanical systems have been studied using information-theoretic measures of Shannon entropy and Fisher information [1]
The new uncertainty relation is based on probabilistic uncertainty measurement that currently exists as entropic uncertainty proposed in the concept of Shannon entropy in the form of
The authors observed that Shannon entropy in the momentum space decreases for narrower mass width, while in the position space Shannon entropy increases for narrower mass width

Summary

Introduction

Various quantum mechanical systems have been studied using information-theoretic measures of Shannon entropy and Fisher information [1]. Studied information-theoretic measures for the solitonic profile mass Schrödinger equation with a squared hyperbolic cosecant potential and deduced a decrease in Shannon entropy in the position space for narrower mass width and an increase in the momentum space for narrower mass width. Onate et al [10] studied the solutions of the 3-dimensional Schrödinger equation together with Shannon entropy and Fisher information under Eckart Manning–Rosen potential. 3. Theoretical quantities and the hyperbolical exponential-type potential theoretical quantities such as Shannon entropy, Onicescu information energy, and Fisher information are calculated. Theoretical quantities and the hyperbolical exponential-type potential theoretical quantities such as Shannon entropy, Onicescu information energy, and Fisher information are calculated The results of these three quantities can be used to calculate the complexity measures.

Onicescu information energy

Fisher information

Complexity measure C

Discussion

Conclusion