Quarkonium masses in a hot QCD medium using conformable fractional of the Nikiforov–Uvarov method

Abu‐Shady, M.

doi:10.1142/s0217751x19502014

Cited by 25 publications

(25 citation statements)

References 30 publications

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“…Fractional-order derivative is basically a natural extension of ordinary derivatives, which has become a popular research topic in applied sciences [1][2][3][4] and engineering [5,6]. The nonlocality plays a significant role in fractional derivative models.…”

Section: Introductionmentioning

confidence: 99%

On a Relativistic Quark Model Description via the Fractional Nikiforov-Uvarov Method

Abu-Shady¹,

Kaabar²

2023

Preprint

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The Dirac equation plays an essential role in the relativistic quantum systems, which is reduced to a form similar to Schrodinger equation when a certain potential's type is selected as the Cornell potential. By choosing the generalized fractional derivative, the fractional Nikiforov-Uvarov method is applied as a good efficient tool. The energy eigenvalues and corresponding wave functions are obtained in the sense of fractional forms by solving Dirac equation analytically. The special case is obtained, which is compatible with the classical model. Solving the fractional Dirac equation will open a new path to solve and improve results in the classical relativistic quantum systems.

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Section: Introductionmentioning

confidence: 99%

On a Relativistic Quark Model Description via the Fractional Nikiforov-Uvarov Method

Abu-Shady¹,

Kaabar²

2023

Preprint

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“…[ 20 ], the fractional SE for a particle with position-dependent mass in an infinite potential well was studied using the CFD. In the context of the CFD, the N -dimensional radial SE was used to investigate the properties of heavy quarkonia for the dependent temperature potential [ 21 ], Trigonometric Rosen–Morse potential [ 22 ], hot-magnetized interaction potential [ 23 ], and generalized Cornell potential [ 24 ]. The impact of fraction-order and dimensional number on heavy-quarkonium masses was also examined.…”

Section: Introductionmentioning

confidence: 99%

The generalized fractional NU method for the diatomic molecules in the Deng–Fan model

2022

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A solution of the fractional N-dimensional radial Schrödinger equation (SE) with the Deng–Fan potential (DFP) is investigated by the generalized fractional Nikiforov–Uvarov (NU) method. The analytical formulas of energy eigenvalues and corresponding eigenfunctions for the DFP are generated. Furthermore, the current results are applied to several diatomic molecules (DMs) for the DFP as well as the shifted Deng–Fan potential (SDFP). For both the DFP and its shifted potential, the effect of the fractional parameter ($${\delta }$$ δ ) on the energy levels of various DMs is examined numerically and graphically. We found that the energy eigenvalues are gradually improved when the fractional parameter increases. The energy spectra of various DMs are also evaluated in three-dimensional space and higher dimensions. It is worthy to note that the energy spectrum raises as the number of dimensions increases. In addition, the dependence of the energy spectra of the DFP and its shifted potential on the reduced mass, screening parameter, equilibrium bond length and rotational and vibrational quantum numbers is illustrated. To validate our findings, the energy levels of the DFP and SDFP are estimated at the classical case ($${\delta =1}$$ δ = 1 ) for various DMs and found that they are entirely compatible with earlier studies. Graphical abstract In this study, a new algorithm of the generalized fractional Nikiforov–Uvarov method is employed to obtain new solutions to the fractional N-dimensional radial Schrödinger equation with the Deng–Fan potential. In addition, the results are applied to several diatomic molecules. The impact of the fractional parameter on the energy levels of various diatomic molecules is investigated. We found that the energy of the diatomic molecule is more bounded at lower fractional parameter values than in the classical case.

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“…[20], the fractional SE for a particle with position-dependent mass in an infinite potential well was studied using the CFD. In the context of the CFD, the N -dimensional radial SE was used to investigate the properties of heavy quarkonia for the dependent temperature potential [21], Trigonometric Rosen-Morse potential [22], hot-magnetized interaction potential [23], and generalized Cornell potential [24]. The impact of fraction-order and dimensional number on heavy-quarkonium masses was also examined.…”

Section: Introductionmentioning

confidence: 99%

The Generalized Fractional NU Method for the Diatomic Molecules in the Deng-Fan Model

Abu-Shady¹,

Abdel-Karim²,

Khokha³

2022

Preprint

Self Cite

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A solution of the fractional N -dimensional radial Schrödinger equation (SE) with the Deng-Fan potential (DFP) is investigated by the generalized fractional NU method. The analytical formulas of energy eigenvalues and corresponding eigenfunctions for the DFP are generated. Furthermore, the current results are applied to several diatomic molecules (DMs) for the DFP as well as the shifted Deng-Fan potential (SDFP). For both the DFP and its shifted potential, the effect of the fractional parameter (δ) on the energy levels of various DMs is examined numerically and graphically. We found that the energy eigenvalues are gradually improved when the fractional parameter increases. The energy spectra of various DMs are also evaluated in three-dimensional space and higher dimensions. It's worthy to note that the energy spectrum raises as the number of dimensions increases. In addition, the dependence of the energy spectra of the DFP and its shifted potential on the reduced mass, screening parameter, equilibrium bond length, rotational and vibrational quantum numbers is illustrated. To validate our findings, we estimate the energy levels of the DFP and SDFP at the classical case (δ = 1) for various DMs and found that they are entirely compatible with earlier studies.

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Quarkonium masses in a hot QCD medium using conformable fractional of the Nikiforov–Uvarov method

Cited by 25 publications

References 30 publications

On a Relativistic Quark Model Description via the Fractional Nikiforov-Uvarov Method

On a Relativistic Quark Model Description via the Fractional Nikiforov-Uvarov Method

The generalized fractional NU method for the diatomic molecules in the Deng–Fan model

The Generalized Fractional NU Method for the Diatomic Molecules in the Deng-Fan Model

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