Introducing time-dependant sources for solving time-domain Schrödinger equation using FDTD method

A numerical approach to introduce excitations in finite-difference time-domain (FDTD) method that solves time-domain Schrödinger equation is presented in this paper. The proposed approach which used to solve electromagnetic waves incidence has its novel application in this study. It can ensure incident electron wave propagate in a designated direction. The corresponding three-dimensional FDTD formulations and modified formulations at the incident boundary are both derived. To verify the proposed method, transmission coefficient of tunneling structures is calculated and the simulation results show high accuracy compared with the analytical solutions. Therefore this approach is proven versatile in solving the time-domain Schrödinger equation and it gives an effective method to analyze other more complicated structures and lays the foundation for future research work in related areas.