High order SF-SFDTD method for solving the time-dependent Schrödinger equation

A high-order spatial filtering-symplectic finite difference time domain (SF-SFDTD) scheme with controllable stability condition is proposed to solve the time-dependent Schrödinger equation (TDSE). Firstly, the higher-order symplectic framework for the discretization of Schrödinger equation is described, and then the spatial filtering method is carried out to extend the stability of the standard SFDTD method. Finally, a numerical example is given to evaluate the correctness of the SF-SFDTD method in numerical solving Schrödinger equation.