Spin-one (1 + 3)-dimensional DKP equation with modified Kratzer potential in the non-commutative space

Saidi, Abdelali; Sedra, M. B.

doi:10.1142/s0217732320500145

Cited by 43 publications

(16 citation statements)

References 80 publications

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“…These data allow us to rewrite the usual radial Klein-Gordon equation in Eq. (13.1) in the ERQM symmetries as follows [54][55][56][57][76][77][78][79][80][81][82][83][84][85]:…”

Section: Review Of Bopp's Shift Methodsmentioning

confidence: 99%

“…This is known by Bopp's shifts and this quantization procedure is called Bopp quantization [85][86][87]. It is known to the specialists that Bopp's shift method has been applied effectively and has succeeded in simplifying the three basic equations: the deformed Klein-Gordon equation [54][55][56][57][76][77][78][79][80][81][82][83][84][85], deformed Dirac equation [88][89][90][91], deformed Schrödinger equation [92][93][94][95] and Duffin-Kemmer-Petiau equation [81,82] with the notion of star product to the Klein-Gordon equation, the Dirac equation and the Schrödinger equation with the notion of ordinary product. Thus, Bopp's shift method is based on reducing second order linear differential equations of the deformed Klein-Gordon equation, the deformed Dirac equation, and the deformed Schrödinger equation with star product to second-order linear differential equations of Klein-Gordon equation, Dirac equation, and Schrödinger equation without star product with simultaneous translation in the space-space.…”

Section: Review Of Bopp's Shift Methodsmentioning

confidence: 99%

“…The CNCCRs with star product in Eqs. (2.1) and (2.2) become new CNCCRs without the notion of star product as follows (see, e.g., [54][55][56][57][76][77][78][79][80][81][82][83][84][85]):…”

Section: Review Of Bopp's Shift Methodsmentioning

confidence: 99%

See 2 more Smart Citations

Diatomic molecules and fermionic particles with improved Hellmann-generalized Morse potential through the solutions of the deformed Klein-Gordon, Dirac and Schrödinger equations in extended relativistic quantum mechanics and extended nonrelativistic quantum mechanics symmetries

Maireche

2022

Rev. Mex. Fís.

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In this paper, we investigate the new approximate bound state solution of deformed Klein--Gordon, Dirac and Schr\"{o}dinger equations in the symmetries of extended relativistic quantum mechanics ERQM and extended nonrelativistic quantum mechanics ENRQM have been obtained with a newly proposed potential called improved Hellmann-generalized Morse potential (IHGMP, for short). To the best of our knowledge, this problem is examined in literature in the usual RQM and NRQM with Hellmann-generalized Morse potential. The potential is a superposition of Hellmann potential, generalized Morse or Deng-Fan potential, and some other exponential terms. By employing the improved approximation to deal with the centrifugal term, Bopp's shift and standard perturbation theory method. The new approximate analytical energy shift and the corrections of bound state energyeigenvalues in ERQM and ENRQM are obtained for some selected diatomic molecules such as (HCl, LiH, H2, ScH, TiH, VH, CrH, CuLi, TiC, NiC, ScN and ScF). The new values that we get appeared sensitive to the quantum numbers $% \left( j,l,s,m\right) $, the potential depths of the improved Hellmann-generalized Morse potential ($a,b$), the range of the potential $%\alpha $, the dissociation energy $D_{e}$, the equilibrium bond length $%r_{e} $, and noncommutativity parameters$\left( \Theta ,\sigma ,\chi \right)$ . We have highlighted three physical phenomena that automatically generate a result of the topological properties of noncommutativity, the first physical phenomena are the perturbative spin-orbit coupling, the second the magnetic induction while the third corresponds to the rotational proper phenomena. In both relativistic and nonrelativistic problems, we show thatthe corrections on the spectrum energy are smaller than the main energy in the ordinary cases of quantum field theory and quantum mechanics. In the new symmetries of NCQM, it is not possible to get the exact analytical solutions for $l=0$ and $l\neq 0$, the approximate solutions are available. Four special cases, i.e., l wave are investigated in the context of deformed Klien-Gordon and Schr\"{o}dinger theories. The relativistic energy equations and the new nonrelativistic energy for some potentials such as improved Hellmann potential and improved generalized Morse potential have also been obtained by varying some potential parameters. We have clearly shown that the Schr\"{o}dinger and Klein Gordon equations in the new symmetries canphysically describe each of the two Dirac equations and the Duffin--Kemmer equation under the effect of IHGMP.

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“…These data allow us to rewrite the usual radial Klein-Gordon equation in Eq. (13.1) in the ERQM symmetries as follows [54][55][56][57][76][77][78][79][80][81][82][83][84][85]:…”

Section: Review Of Bopp's Shift Methodsmentioning

confidence: 99%

Section: Review Of Bopp's Shift Methodsmentioning

confidence: 99%

See 1 more Smart Citation

Diatomic molecules and fermionic particles with improved Hellmann-generalized Morse potential through the solutions of the deformed Klein-Gordon, Dirac and Schrödinger equations in extended relativistic quantum mechanics and extended nonrelativistic quantum mechanics symmetries

Maireche

2022

Rev. Mex. Fís.

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“…Eq. ( 9)); thus, the radial wave function U nl (r) in the RNCQM symmetries becomes as follows [56][57][58][59][60][61][62][63][64][65][66][67]:…”

Section: The Solution Of Dkge Under Modified Manning-rosen Potential In Rncqmmentioning

confidence: 99%

“…is the nonrelativistic effective potential in ordinary NRQM. The radial wave function U nl (r) in nonrelativistic noncommutative three-dimensional real space NRNCQM symmetries becomes as follows [56][57][58][59][60][61][62][63][64][65][66][67]:…”

Section: Nonrelativistic Spectrum Under the Modified Manning-rosen Potentialmentioning

confidence: 99%

A theoretical study of the modified equal scalar and vector Manning-Rosen potential within the deformed Klein-Gordon and Schrödinger in RNCQM and NRNCQM symmetries

Maireche

2021

Rev. Mex. Fís.

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In this research work, within the framework of relativistic and nonrelativistic noncommutative quantum mechanics, the deformed Klein–Gordon and Schrödinger equations were solved with the modified equal vector scalar Manning-Rosen potential that has been of signiﬁcance interest in recent years using Bopp's shift method and standard perturbation theory in the first-order in the noncommutativity parameters in 3-dimensions noncommutative quantum mechanics. By employing the improved approximation of the centrifugal term, the relativistic and nonrelativistic bound state energies were obtained for some diatomic molecules such as (HCl, CH, LiH, CO, NO, O2, I2, N2, H2, and Ar2). The obtained energy eigenvalues appear as a function of the generalized Gamma function, the parameters of noncommutativity, and the parameters of studied potential, in addition to the atomic quantum numbers . In both relativistic and nonrelativistic problems, we show that the corrections on the spectrum energy are smaller than the main energy in the ordinary cases of RQM and NRQM. A straightforward limit of our results to ordinary quantum mechanics shows that the present result is consistent with what is obtained in the literature. We have seen that the improved approximation of the centrifugal term is better than the other approximations in ﬁnding the approximate analytical solutions of the Klein-Gordon and Schrödinger equations for the modified Manning–Rosen potential in RNCQM and NRNCQM.

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Modified Unequal Mixture Scalar Vector Hulthén–Yukawa Potentials Model as a Quark–Antiquark Interaction and Neutral Atoms via Relativistic Treatment Using the Improved Approximation of the Centrifugal Term and Bopp’s Shift Method

Maireche

2020

Few-Body Syst

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Spin-one (1 + 3)-dimensional DKP equation with modified Kratzer potential in the non-commutative space

Cited by 43 publications

References 80 publications

Diatomic molecules and fermionic particles with improved Hellmann-generalized Morse potential through the solutions of the deformed Klein-Gordon, Dirac and Schrödinger equations in extended relativistic quantum mechanics and extended nonrelativistic quantum mechanics symmetries

Diatomic molecules and fermionic particles with improved Hellmann-generalized Morse potential through the solutions of the deformed Klein-Gordon, Dirac and Schrödinger equations in extended relativistic quantum mechanics and extended nonrelativistic quantum mechanics symmetries

A theoretical study of the modified equal scalar and vector Manning-Rosen potential within the deformed Klein-Gordon and Schrödinger in RNCQM and NRNCQM symmetries

Modified Unequal Mixture Scalar Vector Hulthén–Yukawa Potentials Model as a Quark–Antiquark Interaction and Neutral Atoms via Relativistic Treatment Using the Improved Approximation of the Centrifugal Term and Bopp’s Shift Method

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