Fractional Schr\"odinger equation and time dependent potentials

• Main Authors: Gabrick, EC, Sayari, E, de Castro, ASM, Trobia, J, Batista, AM, Lenzi, EK
• Format: Journal Article
• Language: English
• Published: 25-04-2023
• Subjects: Physics - General Physics
• DOI: 10.48550/arxiv.2304.13041

We investigate the solutions for a time dependent potential by considering
two scenarios for the fractional Schr\"odinger equation. The first scenario
analyzes the influence of the time dependent potential in the absence of the
kinetic term. We obtain analytical and numerical solutions for this case by
considering the Caputo fractional time derivative, which extends Rabi's model.
In the second scenario, we incorporate the kinetic term in the Schr\"odinger
equation and consider fractional spatial derivatives. For this case, we analyze
the spreading of the Gaussian wave package under the action of the time and
spatial fractional differential operators.