Solution of time-dependent Shrdinger equation based on finite difference time domain method

The finite difference time domain(FDTD) method is widely used in numerical simulation of electromagnetic fields,and it is combined with quantum mechanics to solve the time-dependent Schrdinger equation.Nevertheless,researches in stability numerical computation often lack theoretical support.This paper mainly deals with the stability condition starting from one-dimensional and multi-dimensional time-dependent Schrdinger equations based on von Neumann stability analysis.Especially,different cases of potential energy are investigated to obtain the expressions.Numerical results show the correctness of the conclusion.