© 2026 Aqora Quantum S.A.S.

Terms Privacy Legal Notice

Symmetry

Thermodynamic Properties of a Diatomic Molecule Under Effects of Small Oscillations in an Elastic Environment

R. L. L. Vitória, C. F. S. Pereira, Sergio Murilo da Silva Braga Martins

Published Jul 2, 2025• 4 citations

Abstract

In this paper, we analytically investigate a diatomic molecule subject to the Morse potential under the small oscillations regime, immersed in a medium with a point defect representing impurities or vacancies in an elastic system. Initially, we apply the small oscillations method to the Morse potential to obtain an analogue to the harmonic potential, and then we solve the generalized Schrödinger equation considering the geometric effects of the defect. The solutions obtained for the bound states reveal that the energy levels and the radial stability point of the molecule are modified by the presence of the defect, depending on the parameters associated with the geometry of the medium. In a second step, we analyze the thermodynamic properties of the system in contact with a thermal reservoir at finite temperature. We derive analytical expressions for the internal energy, Helmholtz free energy, entropy, and specific heat, showing that all these quantities are influenced by the presence of the point defect. The results demonstrate how structural defects alter the quantum and thermodynamic behavior of confined molecules, contributing to the understanding of systems in non-trivial elastic media.

DOI: 10.3390/sym17071038

Related papers

Lennard-Jones Oscillations in an Elastic Environment

José E. S. Bezerra, R. L. L. Vitória, F. M. O. Moucherek

In this purely analytical analysis, we have investigated the effects of a point-like defect in a continuous medium on a diatomic molecule under the influence of small oscillations arising from the Lennard-Jones potential. In the search for bound-state solutions, we have shown that the allowed values for the lowest energy state of the molecule are influenced by the presence of the defect. Furthermore, another quantum effect was observed: the stability radial point of the diatomic molecule depends on the system’s quantum numbers; it is quantized.

AppliedMath•Sep 30, 2025•1 citation

On the doubly anharmonic oscillator in an elastic environment in the presence of a point-like defect

R. L. L. Vitória, Kleber Anderson T. da Silva

Abstract We have investigated a doubly anharmonic oscillator in an elastic medium characterized by the presence of a point-like defect, where we obtain analytically your solution of bound states. We show that it is not possible to obtain a unique expression for the energy profile of the quantum system, but rather an expression corresponding to each radial mode of the system. Furthermore, an interesting quantum effect is presented: the three parameters that characterize the doubly anharmonic oscillator are quantized, that is, they depend on the quantum numbers of the system.

Europhysics Letters (EPL)•Apr 1, 2023•10 citations

Eigensolutions and Thermodynamic Properties of Kratzer plus generalized Morse Potential

Cecilia N. Isonguyo, I. B. Okon, Akaninyene Daniel Antia +6 more

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.

arXiv:2202.09659•Feb 19, 2022•0 citations

Eigensolutions and Thermodynamic Properties of Kratzer Plus Generalized Morse Potential

Cecilia N. Isonguyo, I. B. Okon, Akaninyene Daniel Antia +7 more

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.

Frontiers in Physics•Jul 22, 2022•19 citations

Eigensolutions and Thermodynamic Properties of Kratzer plus generalized Morse Potential

Cecilia N. Isonguyo, I. B. Okon, Akaninyene Daniel Antia +6 more

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

•Mar 17, 2022•0 citations

Algebraic approach to thermodynamic properties of diatomic molecules

Maia N Angelova, Alejandro Frank

A simple model extending Lie algebraic techniques is applied to the analysis of thermodynamic vibrational properties of diatomic molecules. Local anharmonic effects are described by means of a Morse-like potential and the corresponding anharmonic bosons are associated with the SU (2) algebra. The total number of anharmonic bosons, fixed by the potential shape, is determined for a large number of diatomic molecules. A vibrational high-temperature partition function and the related thermodynamic functions are derived and studied in terms of the parameters of the model. The idea of a critical temperature is introduced in relation to the specific heat. A physical interpretation in terms of a quantum deformation associated with the model is given.

Physics of Atomic Nuclei•Oct 1, 2005•15 citations

In this paper, we analytically investigate a diatomic molecule subject to the Morse potential under the small oscillations regime, immersed in a medium with a point defect representing impurities or vacancies in an elastic system. Initially, we apply the small oscillations method to the Morse potential to obtain an analogue to the harmonic potential, and then we solve the generalized Schrödinger equation considering the geometric effects of the defect. The solutions obtained for the bound states reveal that the energy levels and the radial stability point of the molecule are modified by the presence of the defect, depending on the parameters associated with the geometry of the medium. In a second step, we analyze the thermodynamic properties of the system in contact with a thermal reservoir at finite temperature. We derive analytical expressions for the internal energy, Helmholtz free energy, entropy, and specific heat, showing that all these quantities are influenced by the presence of the point defect. The results demonstrate how structural defects alter the quantum and thermodynamic behavior of confined molecules, contributing to the understanding of systems in non-trivial elastic media.

In this purely analytical analysis, we have investigated the effects of a point-like defect in a continuous medium on a diatomic molecule under the influence of small oscillations arising from the Lennard-Jones potential. In the search for bound-state solutions, we have shown that the allowed values for the lowest energy state of the molecule are influenced by the presence of the defect. Furthermore, another quantum effect was observed: the stability radial point of the diatomic molecule depends on the system’s quantum numbers; it is quantized.

Abstract We have investigated a doubly anharmonic oscillator in an elastic medium characterized by the presence of a point-like defect, where we obtain analytically your solution of bound states. We show that it is not possible to obtain a unique expression for the energy profile of the quantum system, but rather an expression corresponding to each radial mode of the system. Furthermore, an interesting quantum effect is presented: the three parameters that characterize the doubly anharmonic oscillator are quantized, that is, they depend on the quantum numbers of the system.

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 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

A simple model extending Lie algebraic techniques is applied to the analysis of thermodynamic vibrational properties of diatomic molecules. Local anharmonic effects are described by means of a Morse-like potential and the corresponding anharmonic bosons are associated with the SU (2) algebra. The total number of anharmonic bosons, fixed by the potential shape, is determined for a large number of diatomic molecules. A vibrational high-temperature partition function and the related thermodynamic functions are derived and studied in terms of the parameters of the model. The idea of a critical temperature is introduced in relation to the specific heat. A physical interpretation in terms of a quantum deformation associated with the model is given.