Abstract: The Crank-Nicolson scheme is presented for solving Schrdinger equation.The Richardson’s extrapolation method is successfully applied to the scheme.Meanwhile，the numerical solution can be gained with accuracy of O(τ4 +h4).This method is shown to be unconditionally stable.The result of numerical experiment shows that the new scheme has higher accuracy than Crank-Nicolson scheme.

Key words: Crank-Nicolson method, Richardson&rsquo, s extrapolation method, Schrdinger equation, truncation error