Version 1
: Received: 2 March 2024 / Approved: 4 March 2024 / Online: 4 March 2024 (10:37:35 CET)
How to cite:
Haouam, I. The Effect of Noncommutative Phase-Space, Local and Nonlocal Potentials on the Current Density in the Context of Minimal Uncertainty in Momentum. Preprints2024, 2024030115. https://doi.org/10.20944/preprints202403.0115.v1
Haouam, I. The Effect of Noncommutative Phase-Space, Local and Nonlocal Potentials on the Current Density in the Context of Minimal Uncertainty in Momentum. Preprints 2024, 2024030115. https://doi.org/10.20944/preprints202403.0115.v1
Haouam, I. The Effect of Noncommutative Phase-Space, Local and Nonlocal Potentials on the Current Density in the Context of Minimal Uncertainty in Momentum. Preprints2024, 2024030115. https://doi.org/10.20944/preprints202403.0115.v1
APA Style
Haouam, I. (2024). The Effect of Noncommutative Phase-Space, Local and Nonlocal Potentials on the Current Density in the Context of Minimal Uncertainty in Momentum. Preprints. https://doi.org/10.20944/preprints202403.0115.v1
Chicago/Turabian Style
Haouam, I. 2024 "The Effect of Noncommutative Phase-Space, Local and Nonlocal Potentials on the Current Density in the Context of Minimal Uncertainty in Momentum" Preprints. https://doi.org/10.20944/preprints202403.0115.v1
Abstract
In this article, we investigate both the Schrödinger and continuity equations in the presence of nonlocal potential that arising from electron-electron interaction and local one in the context of minimal uncertainty in momentum within commutative and noncommutative frameworks. Furthermore, the Frahn–Lemmer potential type is used. Interestingly, the combined effects of both the phase-space noncommutativity and nonlocality on the current density while considering a minimal uncertainty in momentum are examined. We find that the current density, as conventionally defined, does not fulfil the condition of current conservation, thus, a new definition of the current density that encompasses the aforementioned contributions is given. Thereafter, it is shown that the computed current using the new definition of the current density satisfies the current conservation. Noting that using both the product and linear Bopp-Shift, the noncommutativity is inserted.
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
