A high-order compact difference method based on the Richardson extrapolation technique is proposed to solve the Schrdinger equation.For a particular implementation

firstly

numerical results are obtained on the fourth-order compact difference formulas for the second derivatives.Then

the Richardson extrapolation method is used to get an accuracy solution for the Schrdinger equation

which is fourth order in space and fourth order in time.It is proved to be unconditionally stable by Fourier analysis.Numerical experiments are made to demonstrate the high accuracy and validity of this method.