Fractional Quantum Problem Based on Caputo-Fabrizio Derivative

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.

• fractional Schrödinger equation
• Caputo-Fabrizio derivative
• step potential
• reflection coefficient
• transmission coefficient
• fractional differential equations
• wave functions

• 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