Applying fractional quantum mechanics to systems with electrical screening effects

Marwan Al-Raeei

Chaos, Solitons & Fractals, 2021, vol. 150, issue C

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.

Keywords: Fractional Schrödinger Equation; Plasma; Wave function; Screening potential; Colloidal dispersion; Debye-Hückel length; Electrolytes; Tokamak; Fractional parameter; Reduced energy (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:150:y:2021:i:c:s0960077921005634

DOI: 10.1016/j.chaos.2021.111209

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