Space-Time Fractional Schrödinger Equation With Composite Time Fractional Derivative

Abstract

Abstract The fractional Schrödinger equation has recently received substantial attention. We generalize the fractional Schrödinger equation to the Hilfer time derivative and the Caputo space derivative, and solve this equation for an infinite potential by using the Adomian decomposition method. The infinite domain solution of the space-time fractional Schrödinger equation in the case of Riesz space fractional derivative is obtained in terms of the Fox H-functions. We interpret our results for the fractional Schrödinger equation by introducing a complex effective potential in the standard Schrödinger equation, which can be used to describe quantum transport in quantum dots.