Dirac equation and thermodynamic properties with the Modified Kratzer potential

Onyenegecha, Chibueze P.; Njoku, I. J.; Omame, Andrew; Okereke, C. J.; Onyeocha, Emeka

doi:10.1016/j.heliyon.2021.e08023

Cited by 17 publications

(4 citation statements)

References 36 publications

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“…( 77) is the nonrelativistic energy eigenvalue 𝐸 𝑚𝑘 𝑛𝑟 for the modified Kratzer potential consistent with the energy in Refs. [5,83,84] under NRQM symmetries, while the second part is due to the effect of deformation of the space-space for the modified Kratzer potential.…”

Section: The Improved Mie-type Potential Problems In Nreqm Symmetriesmentioning

confidence: 99%

“…Recently, Onyenegecha et al used the formula technique to present the analytic solutions of DE for the modified Kratzer potential under the p-spin and spin symmetries and found the energies analytically and numerically. They also investigated the thermodynamic properties of the 𝑋 1 Σ + 𝑔 state of Cl 2 and N 2 diatomic molecules in the nonrelativistic spin symmetry limit [5]. Under the pspin symmetry, Aydogdu and Sever [6] found an explicit solution of DE for a pseudoharmonic potential in the presence of a linear tensor potential and demonstrated that tensor interactions erase all degeneracies between the members of pseudospin doublets.…”

Section: Introductionmentioning

confidence: 99%

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Deformed Dirac and Shrödinger Equations with Improved Mie-Type Potential for Diatomic Molecules and Fermionic Particles in the Framework of Extended Quantum Mechanics Symmetries

Maireche¹

2022

Ukr. J. Phys.

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In this study, the bound-state solutions of the deformed Dirac equation (DDE) have been determined with the improved Mie-type potential including an improved Coulomb-like tensor potential (IMTPICLP) under the condition of the spin or pseudospin symmetry in the extended relativistic quantum mechanics (ERQM) symmetries. The IMTPICLP model includes a combination of the terms 1/r3 and 1/r4 which coupled with the couplings (LΘ and L̃︀Θ) between the physical properties of the system with the topological deformations of space-space. In the framework of the parametric Bopp’s shift method and standard perturbation theory, the new relativistic and nonrelativistic energy eigenvalues for the improved Mietype potential have been found. The new obtained values appeared sensitive to the quantum numbers (j, k, l,̃︀ l, s, s,̃︀ m, m̃︀ ), the mixed potential depths (A, B, C, α), and noncommutativity parameters (Θ, σ, χ). The new energy spectra of the improved Kratzer–Fues potential within an improved Coulomb-like tensor interaction and the improved modified Kratzer potential within the Coulomb-like tensor interaction have been derived as particular cases of IMTPICLP. We recovered the usual relativistic and nonrelativistic results from the literature by applying the three simultaneous limits (Θ, σ, χ) → (0, 0, 0). One can notice that our results are in close agreement with the recent studies.

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Section: The Improved Mie-type Potential Problems In Nreqm Symmetriesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Deformed Dirac and Shrödinger Equations with Improved Mie-Type Potential for Diatomic Molecules and Fermionic Particles in the Framework of Extended Quantum Mechanics Symmetries

Maireche¹

2022

Ukr. J. Phys.

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“…Schrodinger dengan potensial telah banyak dikaji di antaranya melibatkan potensial Coulomb (Karomah et al, 2021), Osilator Harmonik (Rusmini et al, 2022), Kratzer (Onyenegecha et al, 2021). Selain itu, potensial yang dikaji juga dapat berupa gabungan dari beberpa jenis potensial seperti Hulthen-Hellmann (Akpan et al, 2021), Potensial Quadratik Yukawa dan Eckart (Antia et al, 2020), Wood-Saxon (Suparmi et al, 2021), Hulthen-Non Sentral Posch Teller (Sunarmi et al, 2013) dan lain-lain.…”

Section: Pendahuluanunclassified

Simulasi Penyelesaian Tingkat Energi Sistem Molekul Dalam Pengaruh Potensial Kratzer Dengan Metode Parametrik Nikiforov-Uvarov

Sunarmi

2022

Orb. J. Pend. Ilm. Fis.

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ABSTRAKTelah dilakukan kajian terhadap potensial Kratzer pada sistem molekul dengan menggunakan metode Parametrik Nikiforov-Uvarov. Penelitian bermaksud mendapatkan persamaan tingkat energi sistem dalam pengaruh potensial Kratzer dan melakukan simulasi terhadap persamaan tingkat energi tersebut untuk molekul oksigen, iodin, karbon monoksida, nitrogen monoksida. Penyelesaian tingkat energi sistem diperoleh dengan memisahkan persamaan Schrodinger sistem partikel menjadi 3 bagian yakni radial, zenithal dan azimuthal. Penyelesaian tingkat energi diperoleh dengan meninjau persamaan Schrodinger sistem partikel bagian radial. Penyelesaian persamaan tingkat energi dilakukan dengan menerapkan metode Parametrik Nikiforov-Uvarov. Penyelesaian terhadap persamaan Schrodinger sistem partikel bagian radial dilakukan dengan mereduksi persamaan menjadi persamaan diferensial tipe hipergeometri. Komputasi numerik dan simulasi grafik tingkat energi dilakukan dengan menggunakan Matlab. Berdasarkan hasil penelitian diperoleh penyelesaian persamaan tingkat energi bergantung parameter energi disosiasi, panjang ikatan kesetimbangan, bilangan kuantum serta massa molekul. Molekul iodin memiliki tingkat energi paling rendah dibandingkan molekul oksigen, karbon monoksida, nitrogen monoksida. Kata kunci: tingkat energi; potensial kratzer; metode parametrik nikiforov-uvarov. ABSTRACTA study of the Kratzer potential in molecular systems has been carried out using the Nikiforov-Uvarov Parametric method. The research aims to obtain the energy level equations of the system under the influence of the Kratzer potential and carry out simulations of these energy level equations for oxygen, iodine, carbon monoxide, nitrogen monoxide molecules. The solution for the energy level of the system is obtained by separating the Schrodinger equation of the particle system into 3 parts, namely radial, zenithal and azimuthal. The solution for energy levels is obtained by considering the Schrodinger equation of the radial section particle system. Solving the energy level equation is done by applying the Nikiforov-Uvarov Parametric method. The solution to the Schrodinger equation of the radial section particle system is carried out by reducing the equation to a hypergeometric type differential equation. Numerical computations and graphical simulations of energy levels are carried out using Matlab. Based on the research results, it was found that the solution to the energy level equation depends on the parameters of dissociation energy, equilibrium bond length, quantum number and molecular mass. Iodine molecule has the lowest energy level compared to oxygen molecules, carbon monoxide, nitrogen monoxide. Keywords: energy level; kratzer potential; nikiforov-uvarov parametric method.

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“…Studying thermodynamic properties of systems involves the determination of the partition function. In addition to entropy, specific heat capacity, mean free energy, and others, a partition function allows us to obtain different thermodynamic properties [24,25].…”

Section: Introductionmentioning

confidence: 99%

Study of energies spectra and thermodynamic properties of the relativistic Dirac equation using Feynman path integral method

2023

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In the current paper the contribution of a Coulomb-like potential tensor interaction on the solution of the Dirac equation with a new generalized Morse-like potential is investigated using Feynman path integral method. Relativistic and non-relativistic energy spectra were obtained. Using the resulting non-relativistic energy eigen equations, three diatomic molecules (H2, LiH, and HCl) were investigated and their thermodynamic properties, including mean energy, free energy, entropy, and speciﬁc heat capacity were obtained. A comparison with the available literature shows that the thermodynamic plots obtained match those in the literature.

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Dirac equation and thermodynamic properties with the Modified Kratzer potential

Cited by 17 publications

References 36 publications

Deformed Dirac and Shrödinger Equations with Improved Mie-Type Potential for Diatomic Molecules and Fermionic Particles in the Framework of Extended Quantum Mechanics Symmetries

Deformed Dirac and Shrödinger Equations with Improved Mie-Type Potential for Diatomic Molecules and Fermionic Particles in the Framework of Extended Quantum Mechanics Symmetries

Simulasi Penyelesaian Tingkat Energi Sistem Molekul Dalam Pengaruh Potensial Kratzer Dengan Metode Parametrik Nikiforov-Uvarov

Study of energies spectra and thermodynamic properties of the relativistic Dirac equation using Feynman path integral method

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