Fractional Quantum Problem Based on Caputo-Fabrizio Derivative
Bouzenna Fatma El-Genbazi, Meftah Mohammed T
Abstract
Background and Objective: In the context of the novel definition of the fractional derivative, we solve the Fractional Schrödinger equation based on the non-singular Caputo-Fabrizio derivative definition.The quantum particle is submitted to a step potential.We focus our study to find the reflection and transmission coefficients.Materials and Methods: To reach this goal, we first work out the fractional differential equation defined in terms of the Caputo-Fabrizio derivative.Results: Hence, according to the obtained wave functions of fractional Schrödinger equations, the reflection and transmission coefficient are calculated.Conclusion: Interestingly, our findings collapse to the standard results when the fractional order of derivative become integer numbers.
Details
| Original language | English |
|---|---|
| Journal | Journal of Applied Sciences |
| Volume | 22 |
| Issue number | 1 |
| Pages | 42-47 |
| Publisher | Multidisciplinary Digital Publishing Institute |
| ISSN | 1812-5654 · 1812-5662 |
| DOI | 10.3923/jas.2022.42.47 |
| Publication status | Published — 15 January 2022 |
Keywords
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- Fractional Differential Equations Solutions
- Statistical Mechanics and Entropy
- Quantum Mechanics and Applications
- fractional Schrödinger equation
- Caputo-Fabrizio derivative
- step potential
- reflection coefficient
- transmission coefficient
- fractional differential equations
- wave functions
- Modeling and Simulation
- Statistical and Nonlinear Physics
- Atomic and Molecular Physics, and Optics
- Mathematics
- Physics and Astronomy