A new solution of Schrödinger equation based on symplectic algorithm

An explicit three dimensional symplectic finite-difference time-domain method is introduced to solve the Schrödinger equation. The method is obtained by using a symplectic scheme with a propagator of exponential differential operators for the time direction approximation and fourth-order collocated finite differences for the space discretization. Firstly, a high-order symplectic framework for discretizing the Schrödinger equation is presented. Secondly, the comparisons on numerical stability, dispersion are also provided between the new symplectic scheme and other commonly used methods. Finally, numerical examples are given to evaluate the performance of the proposed method and the advantages on the accuracy and stability are also further demonstrated.