Numerical study for time-fractional Schrödinger equations arising in quantum mechanics

In this paper, we present a semi-analytical technique based on the homotopy analysis transform method (HATM) which is combination of Laplace transform method and the homotopy analysis method (HAM) to solve time-fractional Schrödinger equations. The fractional derivatives are described by Caputo sense. The proposed method presents a procedure of constructing the set of base functions and gives the high order deformation equations in a simple form. The proposed scheme provides solution in the form of a rapidly convergence series. Four examples are given to illustrate the preciseness and effectiveness of the proposed method. The result shows that the HATM is very efficient, simple and can be applied to other nonlinear problems.