Investigations on the Relativistic Interactions in One-Electron Atoms with Modified Yukawa Potential for Spin 1/2 Particles

Maireche, Abdelmadjid

doi:10.18052/www.scipress.com/ifsl.11.29

Cited by 37 publications

(30 citation statements)

References 20 publications

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“…hp ( , , , , , , , ) with spin-1/2 are obtained in this paper on the basis of our original results presented in Eqs. (38), (42), (43) and (42), in addition to the ordinary energy for the Hellmann potential model which is presented in Eq. (9) in the form: 0, , , , , , , ) where the energies of the ground state 0 and the first excited state 1 in the symmetries of quantum mechanics in the Hellmann potential model are as follows:…”

Section: Resultsmentioning

confidence: 99%

“…In this subsection, we want to derive the physical form of the induced Hamiltonian ℎ pert (̂︀,̂︀) due to the space-phase noncommutativity. To achieve this goal, we replace LΘ both and L − by useful physical forms Θ LS and LS, respectively (see, e.g., [39][40][41][42][43]): + + 2 13 ) 1/2 , and ≈ 1/137 is the atomic fine structure constant, and S denotes the spin of the hydrogenic atoms such as (He + , Li +2 , and Be + ). Thus, the spinorbit interactions ℎ (̂︀,̂︀) appear automatically as a result of the deformation of the space phase.…”

Section: Spin-orbit Hamiltonian Operator For the Hydrogenic Atoms In mentioning

confidence: 99%

“…To obtain the exact NC magnetic modifications of the energy for the ground state, the first excited state and ℎ excited states of hydrogenic atoms such as He + , Li +2 , and Be + in the GHP model hp mag (0, , , , , , ), ℎ mag (1, , , , , , ) and ℎ mag ( , , , , , , ) we just replace + or − and (Θ, ) in Eqs. (38), (42) and (43) by the following parameters and ( , ) , respectively:…”

Section: Spin-orbit Hamiltonian Operator For the Hydrogenic Atoms In mentioning

confidence: 99%

See 2 more Smart Citations

A New Approach to the Approximate Analytic Solution of the Three-Dimensional Schrӧdinger Equation for Hydrogenic and Neutral Atoms in the Generalized Hellmann Potential Model

Maireche

2020

Ukr. J. Phys.

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Within the framework of nonrelativistic noncommutative quantum mechanics using the improved approximation scheme to the centrifugal term for any l-states via the generalized Bopp’s shift method and standard perturbation theory, we have obtained the energy eigenvalues of a newly proposed generalized Hellmann potential model (the GHP model) for the hydrogenic atoms and neutral atoms. The potential is a superposition of the attractive Coulomb potential plus Yukawa one, and new central terms appear as a result of the effects of noncommutativity properties of space and phase in the Hellmann potential model. The obtained energy eigen-values appear as a function of the generalized gamma function, the discrete atomic quantum numbers (j, n, l, s and m), infinitesimal parameters (a, b, б) which are induced by the position-position and phase-phase noncommutativity, and, the dimensional parameters (Θ, 0) of the GHP model, in the nonrelativistic noncommutative three-dimensional real space phase (NC: 3D-RSP). Furthermore, we have shown that the corresponding Hamiltonian operator with (NC: 3D-RSP) symmetries is the sum of the Hamiltonian operator of the Hellmann potential model and two operators, the first one is the modified spin-orbit interaction, while the second is the modified Zeeman operator for the hydrogenic and neutral atoms.

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Section: Resultsmentioning

confidence: 99%

Section: Spin-orbit Hamiltonian Operator For the Hydrogenic Atoms In mentioning

confidence: 99%

Section: Spin-orbit Hamiltonian Operator For the Hydrogenic Atoms In mentioning

confidence: 99%

See 1 more Smart Citation

A New Approach to the Approximate Analytic Solution of the Three-Dimensional Schrӧdinger Equation for Hydrogenic and Neutral Atoms in the Generalized Hellmann Potential Model

Maireche

2020

Ukr. J. Phys.

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“…In order to construct a 2D model of NMKP, the essential step is to rewrite the ordinary SE to the new following modified Schrödinger equation (MSE) which play a major role in (NC: 2D-RSP) symmetries [23][24][25][26][27][28][29][30][31][32][33][34]:…”

Section: Theoretical Overview Of Bopp's Shift Methodsmentioning

confidence: 99%

Effects of Two-Dimensional Noncommutative Theories on Bound States Schrödinger Diatomic Molecules under New Modified Kratzer-Type Interactions

Maireche

2017

ILCPA

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Abstract. In this work, an analytical expression for the nonrelativistic energy spectrum of some diatomic molecules was obtained through the Bopp's shift method in the noncommutative (NC) two-dimensional real space-phase symmetries (NC: 2D-RSP) with a new modified Kratzer-type potential (NMKP) in the framework of two infinitesimal parameters θ and θ due to (space-phase) noncommutativity, by means of the solution of the noncommutative Schrödinger equation. The perturbation property of the spin-orbital Hamiltonian operator and new Zeeman effect of twodimensional system are investigated. We have shown that, the new energy of diatomic molecule is the sum of ordinary energy of modified Kratzer-type potential, in commutative space, and new additive terms due to the contribution of the additive part of the NMKP. We have shown also that, the group symmetry of (NC: 2D-RSP) reduce to new sub-group symmetry of NC two-dimensional real space (NC: 2D-RSP) under new modified Kratzer-type interactions.

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“…It is clearly that the above equation including equation (20), the perturbative terms of Hamiltonian operator, which we are subject of discussion in next subsection, we look for a possibility to getting an exact solution of equation (23) including the added new part…”

Section: The Exact Spin-orbital Spectrum For 2d-modified Sextic Dwao Potential In Nc:2d-rsp) For One-electron Atomsmentioning

confidence: 99%

A Theoretical Investigation of the Schrödinger Equation for a Modified Two Dimensional Purely Sextic Double-Well Potential

Maireche¹

2021

Yanbu Journal of Engineering and Science

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A theoretical analytical investigation for the exact solvability of non-relativistic quantum spectrum systems, at low energy for modified two-dimensional purely sextic double-well potential (2D-modified sextic DWAO potential) is discussed, by means Bopp's shift method, instead to solving deformed Schrödinger equation with star product, in the framework of both noncommutativite two dimensional real space and phase (NC: 2D-RSP), the exact corrections for lowest excitations are found straightforwardly for interactions in one-electron atoms by means of the standard perturbation theory for three special cases. Furthermore, the obtained corrections of energies are depended on the four infinitesimals parameters (  ,  ) and ( ,  ),

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Investigations on the Relativistic Interactions in One-Electron Atoms with Modified Yukawa Potential for Spin 1/2 Particles

Abstract: Abstract. Energy levels of one electron atoms have been re-examined by applying an alternative perturbative scheme in solving the modified Dirac equation (m.d.e.) for the modified Yukawa potential model with an arbitrary spin-orbit quantum number

Cited by 37 publications

References 20 publications

A New Approach to the Approximate Analytic Solution of the Three-Dimensional Schrӧdinger Equation for Hydrogenic and Neutral Atoms in the Generalized Hellmann Potential Model

A New Approach to the Approximate Analytic Solution of the Three-Dimensional Schrӧdinger Equation for Hydrogenic and Neutral Atoms in the Generalized Hellmann Potential Model

Effects of Two-Dimensional Noncommutative Theories on Bound States Schrödinger Diatomic Molecules under New Modified Kratzer-Type Interactions

A Theoretical Investigation of the Schrödinger Equation for a Modified Two Dimensional Purely Sextic Double-Well Potential

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