Solution of Dirac Equation with Modified Hylleraas Potential under Spin and Pseudospin Symmetry

Ikot, Akpan N.; Maghsoodi, E.; Awoga, Oladunjoye O.; Zarrinkamar, S.; Hassanabadi, H.

doi:10.12785/qpl/030102

Cited by 8 publications

(3 citation statements)

References 16 publications

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“…The relativistic particles' description with spin (1/2) as in [8] is heavily dependent on the Dirac equation. The Dirac equation has been solved in recent years for various potentials, as seen in literature [9][10][11][12][13][14][15]. The analytical solutions of the Cornell potential with identical scalar and vector potentials to the Dirac equation are examined in [9,10] using the perturbation method and ansatz approach.…”

Section: Introductionmentioning

confidence: 99%

“…The Dirac equation has been solved in recent years for various potentials, as seen in literature [9][10][11][12][13][14][15]. The analytical solutions of the Cornell potential with identical scalar and vector potentials to the Dirac equation are examined in [9,10] using the perturbation method and ansatz approach. For the modified-Hylleraas potential under spin and pseudo spin symmetry limitations, the bound energy spectrum and corresponding generalised hypergeometric wave function of the Dirac equation are found in [5] using the Alhaidari formalism.…”

Section: Introductionmentioning

confidence: 99%

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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%

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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“…Then one can use methods which were developed to solve non-relativistic equations exactly or approximately, such as factorization and path-integral methods [18][19][20][21][22], the Nikiforov-Uvarov method [23], shape invariance [24,25], asymptotic iteration method [26][27][28][29][30], supersymmetric quantum mechanics [31], and so on. For instance, the Dirac equation was solved for the Morse potential [32][33][34][35][36], the harmonic-oscillator potential [37][38][39], the pseudoharmonic potential [40], the Pöschl-Teller potential [41][42][43][44], the Woods-Saxon potential [45,46], the Eckart potential [47,48], the Coulomb and the Hartmann potentials [49], the Hyperbolic potentials and the Coulomb tensor interaction [50,51], the Rosen-Morse potential [52], the Hulthén potential [53][54][55], the Hulthén potential including the Coulomb-like tensor potential [56], the v 0 tanh 2 (r/d) potential [57], the Coulomb-like tensor potential [58], the modified Hylleraas potential [59], the Manning-Rosen and the generalized Manning-...…”

Section: Introductionmentioning

confidence: 99%

Refined comparison theorems for the Dirac equation with spin and pseudo-spin symmetry in d dimensions

Hall

Zorin

2016

Eur. Phys. J. Plus

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The classic comparison theorem of quantum mechanics states that if two potentials are ordered then the corresponding energy eigenvalues are similarly ordered, that is to say if Va ≤ V b , then Ea ≤ E b . Such theorems have recently been established for relativistic problems even though the discrete spectra are not easily characterized variationally. In this paper we improve on the basic comparison theorem for the Dirac equation with spin and pseudo-spin symmetry in d ≥ 1 dimensions. The graphs of two comparison potentials may now cross each other in a prescribed manner implying that the energy values are still ordered. The refined comparison theorems are valid for the ground state in one dimension and for the bottom of an angular momentum subspace in d > 1 dimensions. For instance in a simplest case in one dimension, the condition Va ≤ V b is replaced by Ua ≤ U b , where Ui(x) = x 0 Vi(t)dt, x ∈ [0, ∞), and i = a or b.

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Bound state solutions of Dirac equation with radial exponential-type potentials

Peña

Morales

García-Ravelo

2017

Journal of Mathematical Physics

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In this work, a direct approach for obtaining analytical bound state solutions of the Dirac equation for radial exponential-type potentials with spin and pseudospin symmetry conditions within the frame of the Green and Aldrich approximation to the centrifugal term is presented. The proposal is based on the relation existing between the Dirac equation and the exactly solvable Schrödinger equation for a class of multi-parameter exponential-type potential. The usefulness of the present approach is exemplified by considering some known specific exponential-type potentials which are obtained as particular cases from our proposal. That is, instead of solving the Dirac equation for a special exponential potential, by means of a specialized method, the energy spectra and wave functions are derived directly from the proposed approach. Beyond the applications considered in this work, our proposition could be used as an alternative way in the search of bound state solutions of the Dirac equation for other potentials as well as it can be easily adapted to other approximations to the centrifugal term.

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Solution of Dirac Equation with Modified Hylleraas Potential under Spin and Pseudospin Symmetry

Cited by 8 publications

References 16 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

Refined comparison theorems for the Dirac equation with spin and pseudo-spin symmetry in d dimensions

Bound state solutions of Dirac equation with radial exponential-type potentials

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