Analytical solutions of the N-dimensional Schrödinger equation with modified screened Kratzer plus inversely quadratic Yukawa potential and thermodynamic properties of selected diatomic molecules

Inyang, E. P.; Ayedun, Funmilayo; Ibanga, Efiong A.; Lawal, K. M.; Okon, I. B.; William, E. S.; Omugbe, E.; Onate, C. A.; Antia, Akaninyene D.; Obisung, Effiong O.

doi:10.1016/j.rinp.2022.106075

Cited by 16 publications

(12 citation statements)

References 40 publications

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“…An essential thermodynamic variable that enables the calculation of additional thermal properties for the system is the partition function (PF). The Boltzmann-Gibbs partition function reads [1]  …”

Section: Thermodynamic Propertiesmentioning

confidence: 99%

“…The partition function (PF) which is dependent on temperature, enables the investigation of the thermodynamic properties (TPs) of a system. The partition function, widely employed in molecular physics and statistical physics, facilitates the computation of various thermodynamic properties such as entropy, specific heat capacity, mean free energy, and others [1]. To analyze the behavior of non-relativistic particles in quantum mechanics, including the properties of the system's elementary particles and the mass distribution of mesons, the Schrodinger equation (SE) needs to be solved [2,3].…”

Section: Introductionmentioning

confidence: 99%

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ENERGY SPECTRA, EXPECTATION VALUES, AND THERMODYNAMICPROPERTIES OF HCl AND LiH DIATOMIC MOLECULES

Inyang

2024

Eurasian phys. tech. j.

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The Schrödinger equation is solved by applying the Nikiforov-Uvarov-Functional Analysis method to the Hulthén plus screened Kratzer Potential. The Greene-Aldrich approximation is employed to determine the closed form expressions for the energy equation and the wave function. The Hellmann-Feynman theorem was employed to calculate the energy spectra and expectation values of various quantum states for diatomic moleculesof HCl and LiH. Subsequently, we employed the energy equation that we had previously derived to compute the partition function, which in turn enabled us to determine the thermodynamic properties associated with the diatomic molecules. The partition function for the diatomic molecules of 2Hand LiHwas calculated at different temperatures. The results indicate that the partition function of the two diatomic molecules rose as the temperature increased.The findings we obtained align with the results documented in the literature.

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Section: Thermodynamic Propertiesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

ENERGY SPECTRA, EXPECTATION VALUES, AND THERMODYNAMICPROPERTIES OF HCl AND LiH DIATOMIC MOLECULES

Inyang

2024

Eurasian phys. tech. j.

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“…The details can be found in Appendix A. The Schrödinger equation of a quantum physical system is characterized by a given potential   V r takes the form [72,73]…”

Section: Analytical Solutions Of the Schrödinger Equation With Eckart...mentioning

confidence: 99%

“…With various analytical techniques, such as the Nikiforov-Uvarov (NU) method [1][2][3][4][5][6][7][8][9][10], the asymptotic iterative method (AIM) [11], the supersymmetric quantum mechanics method (SUSQM) [12], the Nikiforov-Uvarov functional analysis (NUFA) method [13][14][15][16], the series expansion method [17][18][19][20][21], the WKB approximation [22][23][24], and so on [25], the Schrödinger equation (SE) can be solved for a variety of potentials. Our knowledge of the underlying cause of a quantum system is significantly influenced by the analytical solutions to this equation with a physical potential.…”

Section: Introductionmentioning

confidence: 99%

Analytical Solutions to The Schrödinger Equation with Collective Potential Models: Application to Quantum Information Theory

Inyang¹,

Ayedun²,

Ibanga³

et al. 2022

East Eur. J. Phys.

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In this study, the energy equation and normalized wave function were obtained by solving the Schrödinger equation analytically utilizing the Eckart-Hellmann potential and the Nikiforov-Uvarov method. Fisher information and Shannon entropy were investigated. Our results showed higher-order characteristic behavior for position and momentum space. Our numerical results showed an increase in the accuracy of the location of the predicted particles occurring in the position space. Also, our results show that the sum of the position and momentum entropies satisfies the lower-bound Berkner, Bialynicki-Birula, and Mycieslki inequality and Fisher information was also satisfied for the different eigenstates. This study's findings have applications in quantum chemistry, atomic and molecular physics, and quantum physics.

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“…Numerous boundary value problems using partial differential equations (PDEs) with boundary constraints depict a wide range of phenomena, including quantum mechanics, heat, electrostatics, electrodynamics, fluid flow, elasticity, and sound [1][2][3]. One of the well-known types of mathematical analysis is the second-order PDEs.…”

Section: Introductionmentioning

confidence: 99%

Application of differential equation in the field of acoustic

et al. 2023

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The current study examines a classification of physical problems involving the attenuation and propagation of structure and fluid-coupled acoustic waves in a discontinuous waveguide. In acoustics, the response of sound to boundaries is important. Therefore,it is expected that all of the discontinuous waveguide's boundaries have the same walls, which can be either hard or impedance. The impedance and hard walls of the waveguide are mathematically modeled with respective Robin and Neumann boundary conditions together with the second-order fi eld differential equation. The physical challenge is solved using the mode-matching (MM) approach, which also matches the continuity criteria for the acoustic pressure and normal velocities at matching connections. Transmission lossand powers scattering graphs against various frequencies and waveguides dimension parameters are shown to evaluate how well the waveguide predicts the sound to enhance or attenuate for both fluid and structure-borne modes incidents. By reconstructing thematching continuity requirements at matching junctions and using the conserved power identity, the accuracy of the derived algebra is confirmed. The current study has significant implications for improving sound quality for audible applications.

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Analytical solutions of the N-dimensional Schrödinger equation with modified screened Kratzer plus inversely quadratic Yukawa potential and thermodynamic properties of selected diatomic molecules

Cited by 16 publications

References 40 publications

ENERGY SPECTRA, EXPECTATION VALUES, AND THERMODYNAMICPROPERTIES OF HCl AND LiH DIATOMIC MOLECULES

ENERGY SPECTRA, EXPECTATION VALUES, AND THERMODYNAMICPROPERTIES OF HCl AND LiH DIATOMIC MOLECULES

Analytical Solutions to The Schrödinger Equation with Collective Potential Models: Application to Quantum Information Theory

Application of differential equation in the field of acoustic

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