A novel high order time-domain scheme for 2D quantum problem

An explict fourth order finite difference time do-main(FDTD) scheme is applied to quantum simulation. The analysis of stablity and dispersion relation of this technique is presented in this article. A strict time bound is derived to ensure stability. The numerical scheme used here is different from the scheme in electromagnetic field. Several numerical experiments are illustrated to verify the efficiency of the new method. Some useful physics results such as eigenfrequency and eigenenergy are also obtained.