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Eigensolutions and Thermodynamic Properties of Kratzer plus generalized Morse Potential

Cecilia N. Isonguyo, I. B. Okon, Akaninyene Daniel Antia, K. J. Oyewumi, E. Omugbe, C. A. Onate, Roseline U. Joshua, M. E. Udoh, Eno E. Ituen

Published Mar 17, 2022• 0 citations
Publisher

Abstract

Abstract In this study, we apply the parametric Nikiforov-Uvarov method to obtain the bound state solution of Schrödinger wave equation in the presence of Kratzer plus generalized Morse potential (KPGM). The energy eigen equation and the corresponding normalised wave function were obtained in closed form. The resulting energy eigen equation were use to study partition function and other thermodynamic properties such as vibrational mean energy, vibrational specific heat capacity, vibrational mean free energy and vibrational entropy for the proposed potential as applied to lithium hydride diatomic molecule. The thermodynamic plots obtained were in excellent agreement to work of existing literatures. The wave function and probability density plots for the diatomic molecules were obtained through a well designed and implemented maple programme.PACS Nos: 03.65Ge; 03.65-w; 03.65Ca

DOI
10.21203/rs.3.rs-1455049/v1

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Abstract In this study, we apply the parametric Nikiforov-Uvarov method to obtain the bound state solution of Schrödinger wave equation in the presence of Kratzer plus generalized Morse potential (KPGM). The energy eigen equation and the corresponding normalised wave function were obtained in closed form. The resulting energy eigen equation were use to study partition function and other thermodynamic properties such as vibrational mean energy, vibrational specific heat capacity, vibrational mean free energy and vibrational entropy for the proposed potential as applied to lithium hydride diatomic molecule. The thermodynamic plots obtained were in excellent agreement to work of existing literatures. The wave function and probability density plots for the diatomic molecules were obtained through a well designed and implemented maple programme.PACS Nos: 03.65Ge; 03.65-w; 03.65Ca
In this study, we apply the parametric Nikiforov-Uvarov method to obtain the bound state solution of Schrödinger wave equation in the presence of Kratzer plus generalized Morse potential (KPGM). The energy eigen equation and the corresponding normalised wave function were obtained in closed form. The resulting energy eigen equation was used to study partition function and other thermodynamic properties such as vibrational mean energy, vibrational specific heat capacity, vibrational mean free energy and vibrational entropy for the proposed potential as applied to lithium hydride diatomic molecule. The thermodynamic plots obtained were in excellent agreement to work of existing literatures. The wave function and probability density plots for the diatomic molecules were obtained through a well designed and implemented maple programme.
In this study, we apply the parametric Nikiforov-Uvarov method to obtain the bound state solution of Schrodinger wave equation in the presence of Kratzer plus generalized Morse potential (KPGM). The energy eigen equation and the corresponding normalised wave function were obtained in closed form. The resulting energy eigen equation were use to study partition function and other thermodynamic properties such as vibrational mean energy, vibrational specific heat capacity, vibrational mean free energy and vibrational entropy for the proposed potential as applied to lithium hydride diatomic molecule. The thermodynamic plots obtained were in excellent agreement to work of existing literatures. The wave function and probability density plots for the diatomic molecules were obtained through a well designed and implemented maple programme.
In this work, we proposed a screened modified Krazer potential and use the newly proposed Nikiforov-Uvarov-Functional Analysis (NUFA) method to obtain the energy spectrum and the corresponding wave function. With the obtained energy spectrum, we studied the numerical results for some selected diatomic molecules and our results are in good agreement with other analytical method. We also evaluated the vibrational partition function for , and diatomic molecules via the Euler–Maclaurin approach and other thermodynamic functions such as free energy, entropy, mean energy and specific heat Capacity. The expectations values of and are also calculated numerically for different diatomic molecules using the normalized wave function for the two low lying states corresponding to the ground and first excited states. Our numerical results for the selected diatomic molecules validate the Heisenberg uncertainty relation, .
Abstract In this paper, the bound state solution of the non-relativistic wave equation with a molecular potential function has been obtained in a closed-form using the Nikiforov-Uvarov method. The solutions of the bound state are then applied to study the information-theoretic measures such as the one-dimensional Shannon and Renyi entropic densities. The expectation values for ⟨r⟩⟨r⟩⟨r⟩, ⟨r2⟩,⟨{r}^{2}⟩,⟨r2⟩, and ⟨p2⟩⟨{p}^{2}⟩⟨p2⟩ were obtained to verify Heisenberg’s uncertainty principle. Utilizing the energy spectrum equation, the thermodynamic vibrational partition function is obtained via the Poisson summation. Other thermodynamic function variations with absolute temperature have been obtained numerically for four diatomic molecules (H2, N2, O2, and HF). The Shannon global entropic sum inequality has also been verified. The Renyi sum for constrained index parameters satisfies the global entropic inequality. The thermodynamic properties of the four molecules are similar and conform to works reported in the existing literature. The obtained vibrational energies are in fair agreement with the ones obtained using other forms of potential energy. The result further indicates that the lowest bounds for the Shannon, Renyi, and Heisenberg inequalities are ground states phenomena.
Abstract The equation of Schrodinger is a fundamental mathematical framework used to clarify the motion of the wave form, which is a phenomenon in the field of quantum physics. A method's wave function contains the complete description of its particles. The computational solution of the Schrodinger problem is a multifaceted problem. The eigenvalues and typical functions of the modified Kratzer plus Hulthen potential were ascertained analytically in this study. This study used an estimating approach that Nikiforov-Uvarov functional analysis had suggested for dealing with the problem. Estimating energy spectra and applying the results to certain specific diatomic molecules was the aim. The excellent results obtained from this strategy were confirmed by comparing our eigenvalue data with additional numerical data that was gathered by other researchers.
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.