Shannon entropy for Feinberg–Horodecki equation and thermal properties of improved Wei potential model

Clement Atachegbe Onate,Ituen Bassey Okon,Michael Chukwudi Onyeaju

doi:10.1515/phys-2021-0038

Clement Atachegbe Onate, Ituen Bassey Okon + Show 1 more

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https://doi.org/10.1515/phys-2021-0038

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Abstract

Abstract We solved a one-dimensional time-dependent Feinberg–Horodecki equation for an improved Wei molecular energy potential function using the parametric Nikiforov–Uvarov method. The quantized momentum and the corresponding wave functions were obtained. With the help of the wave functions obtained, we calculated Shannon entropy for both the position space and momentum space. The results were used to study four molecules. The results of Shannon entropy were found to be in excellent agreement with those found in the literature. For more usefulness of these studies, the quantized momentum obtained was transformed into an energy equation with certain transformations. The energy equation was then used to calculate some thermodynamic properties such as vibrational mean energy, vibrational specific heat, vibrational mean free energy, and vibrational entropy via computation of the partition function. The thermodynamic properties studied for CO, NO, CH, and ScH showed that for a certain range of the temperature studied, the molecules exhibited similar features except for the vibrational entropy.

Highlights

We solved a one-dimensional time-dependent Feinberg–Horodecki equation for an improved Wei molecular energy potential function using the parametric Nikiforov–Uvarov method
The result of the Feinberg–Horodecki equation was used to study Shannon entropy as a theoretic quantity and the results were found to obey the Bialynicki–Birula and Mycielski inequalities, which is in agreement with the study under the time-independent Schrödinger equation
The thermodynamic properties of the molecular energy potential function were calculated for CO, NO, CH, and ScH molecules using their molecular spectroscopic parameters

Summary

Introduction

Abstract: We solved a one-dimensional time-dependent Feinberg–Horodecki equation for an improved Wei molecular energy potential function using the parametric Nikiforov–Uvarov method. The quantized momentum and the corresponding wave functions were obtained. With the help of the wave functions obtained, we calculated Shannon entropy for both the position space and momentum space. The results were used to study four molecules. The results of Shannon entropy were found to be in excellent agreement with those found in the literature. For more usefulness of these studies, the quantized momentum obtained was transformed into an energy equation with certain transformations. The energy equation was used to calculate some thermodynamic properties such as vibrational mean energy, vibrational specific heat, vibrational mean free energy, and vibrational entropy via computation of the partition function. The thermodynamic properties studied for CO, NO, CH, and ScH showed that for a certain range of the temperature studied, the molecules exhibited similar features except for the vibrational entropy

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