M. Moumni - Profile on Academia.edu (original) (raw)
Papers by M. Moumni
Modern Physics Letters A
In this study, we investigate the Pauli oscillator in a noncommutative space. In other words, we ... more In this study, we investigate the Pauli oscillator in a noncommutative space. In other words, we derive wave function and energy spectrum of a spin half non-relativistic charged particle that is moving under a constant magnetic field with an oscillator potential in noncommutative space. We obtain critical values of the deformation parameter and the magnetic field, which they counteract the normal and anomalous Zeeman effects. Moreover, we find that the deformation parameter has to be smaller than [Formula: see text]. Then, we derive the Helmholtz free energy, internal energy, specific heat and entropy functions of the Pauli oscillator in the non commutative space. With graphical methods, at first, we compare these functions with the ordinary ones, and then, we demonstrate the effects of magnetic field on these thermodynamic functions in the commutative and noncommutative space, respectively.
We study space-time non-commutativity applied to the hydrogen atom and the corrections induced to... more We study space-time non-commutativity applied to the hydrogen atom and the corrections induced to transitions frequencies. By writing the Dirac equation for noncommutative Coulomb potential, we compute noncommutative corrections of the energy levels using perturbation methods and by comparing to the Lamb shift accuracy we get a bound on the parameter of noncommutativity. We use this bound to study the effects on the Lyman-α ray and by induction look the possible influence of non-commutativity on some astrophysical and cosmological phenomena.
![Research paper thumbnail of Erratum: “Bosonic oscillator under a uniform magnetic field with Snyder-de Sitter algebra” [J. Math. Phys. 60, 013505 (2019)]](https://attachments.academia-assets.com/118203064/thumbnails/1.jpg)
](Journal of Mathematical Physics, 2020
An error occurred during the transcription of the energies of Eq. (38) in Fig. 1 in Ref. 1 [Eq. (... more An error occurred during the transcription of the energies of Eq. (38) in Fig. 1 in Ref. 1 [Eq. (38) is correct]. The figure representing the energy level spacing of the KG oscillator under a strong magnetic field in Snyder-de Sitter algebra vs the quantum number n is the following (we use the units ̵ h = c = ke = m = 1 and e 2 = α = 1/137): FIG. 1. ΔEn, 0 vs the quantum number n for different values of the deformation parameters α 1 and α 2 (ω = B = 1).
Physica Scripta, 2019
In this work, we study the wave equations in 2D Euclidian space for a new non-central potential c... more In this work, we study the wave equations in 2D Euclidian space for a new non-central potential consisting of a Kratzer term and a dipole term V (r, θ) = Qr −1 +Drr −2 +D θ cos(θ)r −2. For Schrodinger equation, we obtain the analytical expressions of the energies and the wave functions of the system. For Klein-Gordon and Dirac equations, we do the study in both spin and pseudo-spin symmetries to get the eigenfunctions and the eigenvalues. We also study the dependence of energies on the parameters Dr and D θ. We find that the D θ term tends to dissociate the system, and thus counteracts the Coulomb binding effect, and that the Dr term can either amplify or decrease this effect according to its sign.
Relativistic spectrum of hydrogen atom in the space-time non-commutativity
AIP Conference Proceedings, 2012
Journal of Geometry and Physics, 2011
We study space-time noncommutativity applied to the hydrogen atom and the phenomenological aspect... more We study space-time noncommutativity applied to the hydrogen atom and the phenomenological aspects induced. We find that the noncommutative effects are similar to those obtained by considering the extended charged nature of the proton in the atom. To the first order in the noncommutative parameter, it is equivalent to an electron in the fields of a Coulomb potential and an electric dipole and this allows us to get a bound for the parameter. In a second step, we compute noncommutative corrections of the energy levels and find that they are at the second order in the parameter of noncommutativity. By comparing our results to those obtained from experimental spectroscopy, we get another limit for the parameter.
International Journal of Modern Physics A, 2013
We study the corrections induced by the theory of noncommutativity, in both space–space and space... more We study the corrections induced by the theory of noncommutativity, in both space–space and space–time versions, on the spectrum of hydrogen-like atoms. For this, we use the relativistic theory of two-particle systems to take into account the effects of the reduced mass, and we use perturbation methods to study the effects of noncommutativity. We apply our study to the muon hydrogen with the aim to solve the puzzle of proton radius [R. Pohl et al., Nature466, 213 (2010) and A. Antognini et al., Science339, 417 (2013)]. The shifts in the spectrum are found more noticeable in muon H(μH) than in electron H(eH) because the corrections depend on the mass to the third power. This explains the discrepancy between μH and eH results. In space–space noncommutativity, the parameter required to resolve the puzzle θ ss ≈(0.35 GeV )-2, exceeds the limit obtained for this parameter from various studies on eH Lamb shift. For space–time noncommutativity, the value θ st ≈(14.3 GeV )-2 has been obtain...
Chaos in Quantum Yang-Mills System
We study space-time noncommutativity applied to the hydrogen atom and its phenomenological effect... more We study space-time noncommutativity applied to the hydrogen atom and its phenomenological effects. We find that it modifies the potential part of the Hamiltonian in such a way we get the Kratzer potential instead of the Coulomb one and this is similar to add a dipole potential or to consider the extended charged nature of the proton in the nucleus. By calculating the energies from the Schrödinger equation analytically and computing the fine structure corrections using perturbation theory, we study the modifications of the hydrogen spectrum. We find that it removes the degeneracy with respect to both the orbital quantum number l and the total angular momentum quantum number j; it acts here like a Lamb shift. Comparing the results with the experimental values from spectroscopy, we get a new bound for the space-time non-commutative parameter. We do the same perturbative calculation for the relativistic case and compute the corrections of the Dirac energies; we find that in this case too, the corrections are similar to a Lamb shift and they remove the degeneracy with respect to j ; we get an other bound for the parameter of non-commutativity.
We study space-time non-commutativity applied to the hydrogen atom and the corrections induced to... more We study space-time non-commutativity applied to the hydrogen atom and the corrections induced to transitions frequencies. By writing the Dirac equation for noncommutative Coulomb potential, we compute noncommutative corrections of the energy levels using perturbation methods and by comparing to the Lamb shift accuracy we get a bound on the parameter of noncommutativity. We use this bound to study the effects on the Lyman-α ray and by induction look the possible influence of non-commutativity on some astrophysical and cosmological phenomena.
We study analytically the two-dimensional deformed bosonic oscillator equation for charged partic... more We study analytically the two-dimensional deformed bosonic oscillator equation for charged particles (both spin 0 and spin 1 particles) subject to the effect of an uniform magnetic field. We consider the presence of a minimal uncertainty in momentum caused by the Anti–de Sitter model and we use the Nikiforov–Uvarov (NU) method to solve the system. The exact energy eigenvalues and the corresponding wave functions are analytically obtained for both Klein Gordon and scalar Duffin-Kemmer-Petiau (DKP) cases. For spin 1 DKP case, we deduce the behavior of the DKP equation and write the non-relativistic energies and we show the fundamental role of the spin in this case. Finally, we study the thermodynamic properties of the system. PACS: 03.65.Ge, 03.65.Pm.
Modern Physics Letters A
In this study, we investigate the Pauli oscillator in a noncommutative space. In other words, we ... more In this study, we investigate the Pauli oscillator in a noncommutative space. In other words, we derive wave function and energy spectrum of a spin half non-relativistic charged particle that is moving under a constant magnetic field with an oscillator potential in noncommutative space. We obtain critical values of the deformation parameter and the magnetic field, which they counteract the normal and anomalous Zeeman effects. Moreover, we find that the deformation parameter has to be smaller than [Formula: see text]. Then, we derive the Helmholtz free energy, internal energy, specific heat and entropy functions of the Pauli oscillator in the non commutative space. With graphical methods, at first, we compare these functions with the ordinary ones, and then, we demonstrate the effects of magnetic field on these thermodynamic functions in the commutative and noncommutative space, respectively.
We study space-time non-commutativity applied to the hydrogen atom and the corrections induced to... more We study space-time non-commutativity applied to the hydrogen atom and the corrections induced to transitions frequencies. By writing the Dirac equation for noncommutative Coulomb potential, we compute noncommutative corrections of the energy levels using perturbation methods and by comparing to the Lamb shift accuracy we get a bound on the parameter of noncommutativity. We use this bound to study the effects on the Lyman-α ray and by induction look the possible influence of non-commutativity on some astrophysical and cosmological phenomena.
Journal of Mathematical Physics, 2020
An error occurred during the transcription of the energies of Eq. (38) in Fig. 1 in Ref. 1 [Eq. (... more An error occurred during the transcription of the energies of Eq. (38) in Fig. 1 in Ref. 1 [Eq. (38) is correct]. The figure representing the energy level spacing of the KG oscillator under a strong magnetic field in Snyder-de Sitter algebra vs the quantum number n is the following (we use the units ̵ h = c = ke = m = 1 and e 2 = α = 1/137): FIG. 1. ΔEn, 0 vs the quantum number n for different values of the deformation parameters α 1 and α 2 (ω = B = 1).
Physica Scripta, 2019
In this work, we study the wave equations in 2D Euclidian space for a new non-central potential c... more In this work, we study the wave equations in 2D Euclidian space for a new non-central potential consisting of a Kratzer term and a dipole term V (r, θ) = Qr −1 +Drr −2 +D θ cos(θ)r −2. For Schrodinger equation, we obtain the analytical expressions of the energies and the wave functions of the system. For Klein-Gordon and Dirac equations, we do the study in both spin and pseudo-spin symmetries to get the eigenfunctions and the eigenvalues. We also study the dependence of energies on the parameters Dr and D θ. We find that the D θ term tends to dissociate the system, and thus counteracts the Coulomb binding effect, and that the Dr term can either amplify or decrease this effect according to its sign.
Relativistic spectrum of hydrogen atom in the space-time non-commutativity
AIP Conference Proceedings, 2012
Journal of Geometry and Physics, 2011
We study space-time noncommutativity applied to the hydrogen atom and the phenomenological aspect... more We study space-time noncommutativity applied to the hydrogen atom and the phenomenological aspects induced. We find that the noncommutative effects are similar to those obtained by considering the extended charged nature of the proton in the atom. To the first order in the noncommutative parameter, it is equivalent to an electron in the fields of a Coulomb potential and an electric dipole and this allows us to get a bound for the parameter. In a second step, we compute noncommutative corrections of the energy levels and find that they are at the second order in the parameter of noncommutativity. By comparing our results to those obtained from experimental spectroscopy, we get another limit for the parameter.
International Journal of Modern Physics A, 2013
We study the corrections induced by the theory of noncommutativity, in both space–space and space... more We study the corrections induced by the theory of noncommutativity, in both space–space and space–time versions, on the spectrum of hydrogen-like atoms. For this, we use the relativistic theory of two-particle systems to take into account the effects of the reduced mass, and we use perturbation methods to study the effects of noncommutativity. We apply our study to the muon hydrogen with the aim to solve the puzzle of proton radius [R. Pohl et al., Nature466, 213 (2010) and A. Antognini et al., Science339, 417 (2013)]. The shifts in the spectrum are found more noticeable in muon H(μH) than in electron H(eH) because the corrections depend on the mass to the third power. This explains the discrepancy between μH and eH results. In space–space noncommutativity, the parameter required to resolve the puzzle θ ss ≈(0.35 GeV )-2, exceeds the limit obtained for this parameter from various studies on eH Lamb shift. For space–time noncommutativity, the value θ st ≈(14.3 GeV )-2 has been obtain...
Chaos in Quantum Yang-Mills System
We study space-time noncommutativity applied to the hydrogen atom and its phenomenological effect... more We study space-time noncommutativity applied to the hydrogen atom and its phenomenological effects. We find that it modifies the potential part of the Hamiltonian in such a way we get the Kratzer potential instead of the Coulomb one and this is similar to add a dipole potential or to consider the extended charged nature of the proton in the nucleus. By calculating the energies from the Schrödinger equation analytically and computing the fine structure corrections using perturbation theory, we study the modifications of the hydrogen spectrum. We find that it removes the degeneracy with respect to both the orbital quantum number l and the total angular momentum quantum number j; it acts here like a Lamb shift. Comparing the results with the experimental values from spectroscopy, we get a new bound for the space-time non-commutative parameter. We do the same perturbative calculation for the relativistic case and compute the corrections of the Dirac energies; we find that in this case too, the corrections are similar to a Lamb shift and they remove the degeneracy with respect to j ; we get an other bound for the parameter of non-commutativity.
We study space-time non-commutativity applied to the hydrogen atom and the corrections induced to... more We study space-time non-commutativity applied to the hydrogen atom and the corrections induced to transitions frequencies. By writing the Dirac equation for noncommutative Coulomb potential, we compute noncommutative corrections of the energy levels using perturbation methods and by comparing to the Lamb shift accuracy we get a bound on the parameter of noncommutativity. We use this bound to study the effects on the Lyman-α ray and by induction look the possible influence of non-commutativity on some astrophysical and cosmological phenomena.
We study analytically the two-dimensional deformed bosonic oscillator equation for charged partic... more We study analytically the two-dimensional deformed bosonic oscillator equation for charged particles (both spin 0 and spin 1 particles) subject to the effect of an uniform magnetic field. We consider the presence of a minimal uncertainty in momentum caused by the Anti–de Sitter model and we use the Nikiforov–Uvarov (NU) method to solve the system. The exact energy eigenvalues and the corresponding wave functions are analytically obtained for both Klein Gordon and scalar Duffin-Kemmer-Petiau (DKP) cases. For spin 1 DKP case, we deduce the behavior of the DKP equation and write the non-relativistic energies and we show the fundamental role of the spin in this case. Finally, we study the thermodynamic properties of the system. PACS: 03.65.Ge, 03.65.Pm.