Time dependent solutions for a fractional Schrödinger equation with delta potentials

Abstract

We investigate, for an arbitrary initial condition, the time dependent solutions for a fractional Schrödinger equation in presence of delta potentials by using the Green function approach. The solutions obtained show an anomalous spreading asymptotically characterized by a power-law behavior, which is governed by the order of the fractional spatial operator present in the Schrödinger equation.