Fractional Schrödinger equation and time dependent potentials

Abstract: 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.