A note on the numerical solution of fractional Schrödinger differential equations

Abstract

First and second orders of accuracy difference schemes are presented for a fractional Schrödinger differential equation which is derived from classical Schrödinger differential equation with the first order time derivative changed to a Riemann-Louville fractional derivative. Numerical experiments are carried out on a one-dimensional fractional Schrödinger differential equation. © 2012 American Institute of Physics.