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Applying fractional quantum mechanics to systems with electrical screening effects

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  • Al-Raeei, Marwan

Abstract

In this article, we simulate the spatial form of the fractional Schrödinger equation for the electrical screening potential using Riemann-Liouville definition of the fractional derivatives and the numerical simulation methods. We find the wave function of systems described by the electrical screening interaction potential with a specific electrical permittivity. We find and apply the dimensionless formalism of the spatial fractional Schrödinger equation in case of the electrical screening interaction potential in the stationary state. We find the probabilities and the amplitude of the wave functions for multiple values of the spatial fractional parameter of the fractional Schrödinger equation. In every case of the spatial fractional parameter, we take multiple values of the dimensionless energy. The algorithm of this work is applied in case of the systems which obey the electrical screening interaction potential to be described by the fractional quantum mechanics such as the plasma systems, tokamak and some colloidal dispersion, all we need, the parameters of the system and applying the method.

Suggested Citation

  • Al-Raeei, Marwan, 2021. "Applying fractional quantum mechanics to systems with electrical screening effects," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    • Handle: RePEc:eee:chsofr:v:150:y:2021:i:c:s0960077921005634
    DOI: 10.1016/j.chaos.2021.111209
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    References listed on IDEAS

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    1. Yang, Gaiqiang & Li, Xia & Huo, Lijuan & Liu, Qi, 2020. "A solving approach for fuzzy multi-objective linear fractional programming and application to an agricultural planting structure optimization problem," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    2. Akgül, Ali & Fatima, Umbreen & Iqbal, Muhammad Sajid & Ahmed, Nauman & Raza, Ali & Iqbal, Zafar & Rafiq, Muhammad, 2021. "A fractal fractional model for computer virus dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).
    3. Li, Yuqing & He, Xing & Zhang, Wei, 2020. "The fractional difference form of sine chaotification model," Chaos, Solitons & Fractals, Elsevier, vol. 137(C).
    4. Rui Su & Zhaojian Xu & Jiang Wu & Deying Luo & Qin Hu & Wenqiang Yang & Xiaoyu Yang & Ruopeng Zhang & Hongyu Yu & Thomas P. Russell & Qihuang Gong & Wei Zhang & Rui Zhu, 2021. "Dielectric screening in perovskite photovoltaics," Nature Communications, Nature, vol. 12(1), pages 1-11, December.
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    Cited by:

    1. Ahmed Salem & Lamya Almaghamsi, 2023. "Solvability of Sequential Fractional Differential Equation at Resonance," Mathematics, MDPI, vol. 11(4), pages 1-18, February.
    2. Didier Samayoa & Liliana Alvarez-Romero & José Alfredo Jiménez-Bernal & Lucero Damián Adame & Andriy Kryvko & Claudia del C. Gutiérrez-Torres, 2024. "Torricelli’s Law in Fractal Space–Time Continuum," Mathematics, MDPI, vol. 12(13), pages 1-13, June.
    3. Dmitriy Kvitko & Vyacheslav Rybin & Oleg Bayazitov & Artur Karimov & Timur Karimov & Denis Butusov, 2024. "Chaotic Path-Planning Algorithm Based on Courbage–Nekorkin Artificial Neuron Model," Mathematics, MDPI, vol. 12(6), pages 1-20, March.

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