Two Accurate Semi-analytical Techniques for Solving (2+1)-D and (3+1)-D Schrodinger Equations

Abstract

In this paper, the solutions of the (2+1)-D and (3+1)-D Schrodinger equations are investigated mathematically using two efficient semi-analytical techniques. One proposed technique is based on the combination of the formable transform and the homotopy perturbation method (FTHPM), whereas another technique is the classical variational iteration method (VIM). A comparison study between the formable transform-based homotopy perturbation method (FTHPM) and the variational iteration method (VIM) for solving these equations is discussed. Some theorems are presented to illustrate the convergence of both semi-analytical techniques. To verify the accuracy and efficiency of the proposed schemes, two test examples are discussed.