The Effect of Strong Magnetic Field on Heavy Quarkonia in a Hot Medium Using Nikiforov-Uvarov Method

Abu‐Shady, M.; Fathallah, Hamdi

doi:10.13005/ojps06.01-02.04

Cited by 4 publications

(7 citation statements)

References 61 publications

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“…CONCLUSION By using generalized fractional derivative, we obtained the solution the parametric second-order differential equation by using the NU method which is more effective than the power series method, numerical methods, or approximation methods because we get on good results by using this method as in Refs. [22,23]. The parametric second-order differential equation is the general case and we get the special case when 𝛼 𝛽 1 as in Ref.…”

Section: Case (4): Kratzer-fues Potentialmentioning

confidence: 99%

“…In Ref. [22], the fractional nonrelativistic potential model is used to explore the dissociation of heavy quarkonium in a hot magnetized medium in which the energy eigenvalues and the radial wave functions are obtained. The generalized fractional analytical iteration method is used as in Ref.…”

Section: Introductionmentioning

confidence: 99%

“…This method is very good because we get on a good result compared by another methods as in Refs. [22,23].…”

Section: Introductionmentioning

confidence: 99%

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The Parametric Generalized Fractional Nikiforov-Uvarov Method and Its Applications

Abu-Shady,

Fath-Allah

2023

East Eur. J. Phys.

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By using generalized fractional derivative, the parametric generalized fractional Nikiforov-Uvarov (NU) method is introduced. The second-order parametric generalized differential equation is exactly solved in the fractional form. The obtained results are applied on the extended Cornell potential, the pesudoharmonic potential, the Mie potential, the Kratzer-Fues potential, the harmonic oscillator potential, the Morse potential, the Woods-Saxon potential, the Hulthen potential, the deformed Rosen-Morse potential and the P schl-Teller potential which play an important role in the fields of molecular and atomic physics. The special of classical cases are obtained from the fractional cases at which are agreement with recent works.

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Section: Case (4): Kratzer-fues Potentialmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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The Parametric Generalized Fractional Nikiforov-Uvarov Method and Its Applications

Abu-Shady,

Fath-Allah

2023

East Eur. J. Phys.

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“…The use of fractional calculus has attracted attention in a variety of areas in physics [34][35][36][37][38][39]. For heavy quarkonium systems, methods as the NU formulation and analytical iteration have been explored to provide analytical solutions of the N-dimensional radial Schrödinger equation in the framework of fractional space [35,40]. A category of potentials including the oscillator potential, the Woods-Saxon potential, and the Hulthen potential have also been studied analytically with fractional radial Schrödinger equation by NU method [40,41].…”

Section: Introductionmentioning

confidence: 99%

Fractional Effective Quark-Antiquark Interaction in Symplectic Quantum Mechanics

Luz

Abu‐Shady

Dessano

et al. 2023

Advances in High Energy Physics

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Considering the formalism of symplectic quantum mechanics, we investigate a two-dimensional nonrelativistic strong interacting system, describing a bound heavy quark-antiquark state. The potential has a linear component that is analyzed in the context of generalized fractional derivatives. For this purpose, the Schrödinger equation in phase space is solved with the linear potential. The ground state solution is obtained and analyzed through the Wigner function for the meson c c ¯ . One basic and fundamental result is that the fractional quantum phase-space analysis gives rise to the confinement of quarks in the meson, consistent with experimental results.

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“…Since the higher dimension studies aid in a broad approach to the problem, allowing the desired outcomes in the lower dimensions to be obtained directly by selecting appropriate with N . Therefore, a wide number of works [55][56][57][58][59][60][61][62][63][64][65][66] have been reported to derive the energy spectra of SE solutions in N -dimensional space.…”

Section: Introductionmentioning

confidence: 99%

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

2022

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 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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The Effect of Strong Magnetic Field on Heavy Quarkonia in a Hot Medium Using Nikiforov-Uvarov Method

Cited by 4 publications

References 61 publications

The Parametric Generalized Fractional Nikiforov-Uvarov Method and Its Applications

The Parametric Generalized Fractional Nikiforov-Uvarov Method and Its Applications

Fractional Effective Quark-Antiquark Interaction in Symplectic Quantum Mechanics

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

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