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Eigenfunction, uncertainties and thermal properties of the Schrodinger equation with Screened modified Kratzer potential for diatomic molecules.

Collins Okon Edet, A. N. Ikot, U. S. Okorie, Hewa Yaseen Abdullah, Idris Salah

Published May 31, 2020• 4 citations
Publisher

Abstract

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, .

DOI
10.22541/au.159098050.09308623

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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, .
In this paper, we solved the Schrodinger equation with Hellmann-modified Kratzer potential using Nikiforov-Uvarov-Functional Analysis (NUFA) method. The obtained energy is used to study the numerical results of the ro-vibrational energy spectra for some selected diatomic molecules and their thermodynamic properties. In addition, we also investigated the Fisher information for three diatomic molecules and they all satisfied the Stam-Cramer-Rao inequalities uncertainty relations. Special cases of the potential are discussed and we compute the numerical eigenvalue of the modified Kratzer, Kratzer-Feus and Hellmann potentials for comparison with other analytical methods. The results of the present study agree with the results obtained with other known methods.
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The Schrödinger equation was solved for the Hulthén plus screened Kratzer Potential (HSKP) via the Nikiforov–Uvarov – functional analysis (NUFA) method. The bound-state energy and wave function for the HSKP were obtained in a closed form by applying the Greene–Aldrich approximation scheme to the inverse-square term. Using the resulting energy equation, we computed the energy spectra for 12 diatomic molecules (CuLi, TiH, VH, TiC, HCl, LiH, H2, ScH, CO, I2, N2, and NO) for various quantum states. To show the accuracy of our procedure, four special cases of the collective potential were obtained, and the results are in excellent agreement with the existing literature.
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.
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 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.