Numerical simulation of the space dependent fractional Schrödinger equation for London dispersion potential type

Al‐Raeei, Marwan; El-Daher, Moustafa Sayem

doi:10.1016/j.heliyon.2020.e04495

Cited by 5 publications

(6 citation statements)

References 20 publications

(40 reference statements)

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“…[46], [48], [49]. As can be shown in Tables (10)(11)(12)(13)(14)(15), the ro-vibrational energy spectra of all selected DMs rise as the vibrational and rotational quantum numbers increase. Importantly, one can see that our estimates are perfectly consistent with prior works that used other techniques.…”

Section: Resultsmentioning

confidence: 89%

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

Abu-Shady¹,

Abdel-Karim²,

Khokha³

2022

Preprint

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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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Section: Resultsmentioning

confidence: 89%

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

Abu-Shady¹,

Abdel-Karim²,

Khokha³

2022

Preprint

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“…Al-Raeei and El-Daher relied on the definition of Riemann–Liouville fractional derivative with a numerical technique to solve the space-dependent fractional SE for the Coulomb potential [ 10 ], Van Der Walls potential [ 11 ], Lennard-Jones potential [ 12 ] and Morse potential [ 13 ].…”

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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“…Jonathan Lenells provided foundation for the geometric study of HS equation, this exhibits a geodesic flow. The system of nonlinear DEs like Hunter-Saxton, Camassa-Holm and Degasperis-Procesi was analyzed by variational principle to find the weak solutions in [8] , Volterra-Fredholm integral equations [9] , Boussinesq equations [10] , Schrödinger equation [11] , [12] , telegraph PDEs [13] , [14] , Burgers equation [15] . There are several researches in the literature, that are examined by the different techniques [16] , [17] , [18] , [19] , [20] .…”

Section: Introductionmentioning

confidence: 99%

Numerical computing approach for solving Hunter-Saxton equation arising in liquid crystal model through sinc collocation method

Ahmad

Ilyas

Kutlu

et al. 2021

Heliyon

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In this study, numerical treatment of liquid crystal model described through Hunter-Saxton equation (HSE) has been presented by sinc collocation technique through theta weighted scheme due to its enormous applications including, defects, phase diagrams, self-assembly, rheology, phase transitions, interfaces, and integrated biological applications in mesophase materials and processes. Sinc functions provide the procedure for function approximation over all types of domains containing singularities, semi-infinite or infinite domains. Sinc functions have been used to reduce HSE into an algebraic system of equations that makes the solution quite superficial. These algebraic equations have been interpreted as matrices. This projected that sinc collocation technique is considerably efficacious on computational ground for higher accuracy and convergence of numerical solutions. Stability analysis of the proposed technique has ensured the accuracy and reliability of the method, moreover, as the stability parameter satisfied the condition the proposed solution of the problem converges. The solution of the HSE is presented through graphical figures and tables for different cases that are constructed on various values of and collocation points. The accuracy and efficiency of the proposed technique is analyzed on the basis of absolute errors.

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Numerical simulation of the space dependent fractional Schrödinger equation for London dispersion potential type

Cited by 5 publications

References 20 publications

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

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

Numerical computing approach for solving Hunter-Saxton equation arising in liquid crystal model through sinc collocation method

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