The Investigation of Approximate Solutions of Deformed Klein–Gordon and Schrödinger Equations Under Modified More General Exponential Screened Coulomb Potential Plus Yukawa Potential in NCQM Symmetries

Maireche, Abdelmadjid

doi:10.1007/s00601-021-01639-8

Cited by 18 publications

(10 citation statements)

References 74 publications

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“…In the search for solutions of the NR deformed Schrödinger equation DSE under the influence of several different potentials [56][57][58][59][60][61][62][63][64]. The success of this method was not limited to the DSE, but was extended to the study of various relativistic physics problems, for example, for the DKGE [65][66][67][68][69][70][71], for the DDE [72][73][74][75][76][77][78][79][80] and the deformed DKP equation [81,82]. Thus, the BS method allows us to simplify second-order linear differential equations of the DSE, DKG, DDE, and DDKPE with the Weyl-Moyal star product to the second-order linear differential SE, KGE, DE, and DKP equations with the ordinary product with simultaneous translation in the spacespace.…”

Section: Review Of Bopp's Shift Methodsmentioning

confidence: 99%

The Influence of Deformation Space-Space on High and Low Energy Spectra of Fermionic Particles and Spectra of Heavy Quarkonia with Improved Hulthén Plus Hyperbolic Exponential Inversely Quadratic Potential

Maireche

2023

Ukr. J. Phys.

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In this work, the modified approximation to the centrifugal barrier term is applied to find approximate bound-state solutions of the deformed Dirac equation for the spin and pseudospin symmetries in a model with the improved hyperbolic Hulth´en and hyperbolic exponential inversely quadratic potentials (IHHEIQPs) using the parametric method of Bopp’s shift and the standard perturbation theory in the extended relativistic quantum mechanics (ERQM). Our results indicate that the new energy eigenvalues are highly sensitive to the potential parameters (ν1, A) and to the values of quantum atomicnumbers (j, k, l, m,̃︀ l, ̃︀ m, s, ̃︀s), range of the potential ν, and noncommutativity parameters (θ, σ, β). We found that the effect of a space-space deformation gives a correction in the energy spectrum, where the main energy term remains due to the effect of the hyperbolic Hulth´en and hyperbolic exponential inversely quadratic potentials known in the literature. The new nonrelativistic energies are obtained by applying the nonrelativistic limit to the relativistic spin-energy equation in the extended nonrelativistic quantum mechanics (ENRQM). The proposed potential model reduces to the improved Hulth´en and exponential inversely quadratic potentials as special cases in ERQM. The present results are applied for calculating the new mass spectra Mhiqpnc−nl of heavy mesons such as cc, bb, bc, bs, cs, and bq,q = (u, d) in ENRQM. It turns out that the values of masses come from the contribution of the mass spectra Mhiqpnl in NRQM, while the effect of a space-space deformation δMhiqpnc−nl is an infinitesimal correction as compared with Mhiqpnl. Our results seem to be significant and agree perfectly with the ones in the literature.

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Section: Review Of Bopp's Shift Methodsmentioning

confidence: 99%

The Influence of Deformation Space-Space on High and Low Energy Spectra of Fermionic Particles and Spectra of Heavy Quarkonia with Improved Hulthén Plus Hyperbolic Exponential Inversely Quadratic Potential

Maireche

2023

Ukr. J. Phys.

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“…Here are elements of antisymmetric ( ) real matrices, the effective Planck constant approximatively equal to reduced Planck constant , ( is the infinitesimal parameter NP, and for and ) is just an antisymmetric number while is the Kronecker symbol. The Weyl-Moyal star product of and is , which is generalized to the new deformed form by as follows, [38][39][40][41][42][43][44][45][46][47][48] which can be reduced to in the first order of NP as follows [46][47][48][49][50][51][52][53][54][55] The sum indices equal 1,2 and 3. Physically, the second term in Eq.…”

Section: Tionmentioning

confidence: 99%

Arbitrary (k, l) States-Solutions of the Dirac and Schrödinger Equations Interacting with Improved Spatially-Dependent Mass Coulomb Potential with an improved Coulomb-like tensor interaction Model for H-atoms from 3D-RNCS and 3D-NRNCS symmetries

Maireche

2023

Yanbu Journal of Engineering and Science

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The improved spatially dependent mass Coulomb potential with an improved Coulomb-like tensor interaction (ISDM(CP-CLTI)) model has been used to investigate the new bound state solutions of the deformed Dirac equation under the condition of spin symmetry and pseudospin symmetry in the 3D-relativistic noncommutative space (3D-RNCS) symmetries. The combination of spatially dependent mass Coulomb potential with Coulomb-like tensor interaction (ISDM(CP-CLTI)) and the terms (1/r^3 and 1/r^4 ) which are connected with the induced couplings (LΘ and L ̃Θ) produced from the topological defects of space-space gives ISDM(CP-CLTI) model. The new relativistic and non-relativistic energy eigenvalues for the hydrogen atoms (H-atoms) such as He+, Li+2, and Be3+ under the ISDM(CP-CLTI) model have been derived within the parameters of the parametric Bopp shift method and standard perturbation theory. The new values E_nc^sp(n,C,m_0,m_1,H,Θ,τ,χ,j,l,s,m) and E_nc^ps(n,C,m_0,m_1,H,Θ,τ,χ,j,l,l ̃,s ̃,m ̃) that we obtained appeared to be sensitive to the quantum atomic discrete quantum numbers (j,k,l,s,m,l ̃,s ̃,m ̃), the mixed potential depths (C/q,m_0,m_1,H), and noncommutativity parameters (NP) (Θ,σ,χ). Within the context of relativistic extended quantum mechanics, we have obtained certain significant special cases that, in our view, will be interesting to the specialized researcher. When we applied the three simultaneous limitations (Θ,σ,χ)→(0,0,0), NP we were able to retrieve the typical results of relativistic and non-relativistic cases in the literature. Our new model presented new physical features compared to other models known in the literature.

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“…To perform this task, the physical form of DSE, it is necessary to replace the ordinary three-dimensional Hamiltonian operators 𝐻 𝑥 , 𝑝 , the complex wave function 𝛹 𝑟 → , and energy 𝐸 with the new three Hamiltonian operators𝐻 𝑥 , 𝑝̂ , the new complex wave function𝛹 𝑟→ , and new values𝐸 , respectively. In addition to replacing the ordinary product with the Weyl-Moyal star product, which allows us to construct the DSE in the 3D-NRNCPS symmetries framework as [55][56][57][58][59][60]:…”

Section: Dse Solution For An Improved New Internal Energy Potential A...mentioning

confidence: 99%

The Influence of Deformation Phase-Space on Spectra of Heavy Quarkonia in Improved Energy Potential at Finite Temperature Model of Shrodinger Equation Via the Generalized Boob’s Shift Method and Standard Perturbation Theory

Maireche

2023

East Eur. J. Phys.

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In this work, we obtain solutions of the deformed Schrödinger equation (DSE) with improved internal energy potential at a finite temperature model in a 3-dimensional nonrelativistic noncommutative phase-space (3D-NRNCPS) symmetries framework, using the generalized Bopp’s shift method in the case of perturbed nonrelativistic quantum chromodynamics (pNRQCD). The modified bound state energy spectra are obtained for the heavy quarkonium system such as charmonium cc- and bottomonium bb- at ﬁnite temperature. It is found that the perturbative solutions of the discrete spectrum are sensible to the discreet atomic quantum numbers (j,l,s,m) of the ( QQ- (Q=c,b)) state, the parameters of internal energy potential (T,αs(T), mD (T),β,c), which are the Debye screening mass mD (T), the running coupling constant αs(T) the critical temperature β, the free parameter c in addition to noncommutativity parameters (Θ,θ-). The new Hamiltonian operator in 3D-NRNCPS symmetries is composed of the corresponding operator in commutative phase-space and three additive parts for spin-orbit interaction, the new magnetic interaction, and the rotational Fermi-term. The obtained energy eigenvalues are applied to obtain the mass spectra of heavy quarkonium systems (cc- and bb-). The total complete degeneracy of the new energy levels of the improved internal energy potential changed to become equal to the new value 3n2 in 3D-NRNCPS symmetries instead of the value n2 in the symmetries of 3D-NRQM. Our non-relativistic results obtained from DSE will possibly be compared with the Dirac equation in high-energy physics.

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The Investigation of Approximate Solutions of Deformed Klein–Gordon and Schrödinger Equations Under Modified More General Exponential Screened Coulomb Potential Plus Yukawa Potential in NCQM Symmetries

Cited by 18 publications

References 74 publications

The Influence of Deformation Space-Space on High and Low Energy Spectra of Fermionic Particles and Spectra of Heavy Quarkonia with Improved Hulthén Plus Hyperbolic Exponential Inversely Quadratic Potential

The Influence of Deformation Space-Space on High and Low Energy Spectra of Fermionic Particles and Spectra of Heavy Quarkonia with Improved Hulthén Plus Hyperbolic Exponential Inversely Quadratic Potential

Arbitrary (k, l) States-Solutions of the Dirac and Schrödinger Equations Interacting with Improved Spatially-Dependent Mass Coulomb Potential with an improved Coulomb-like tensor interaction Model for H-atoms from 3D-RNCS and 3D-NRNCS symmetries

The Influence of Deformation Phase-Space on Spectra of Heavy Quarkonia in Improved Energy Potential at Finite Temperature Model of Shrodinger Equation Via the Generalized Boob’s Shift Method and Standard Perturbation Theory

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