中文摘要：

利用4阶精度紧致格式离散1维Schrdinger方程的空间方向,并推广到2维Schrdinger方程问题.在时间方向用P-R ADI方法离散,经理论分析证明该格式具有高精度性、省时性和绝对稳定性,并证明该格式还保持离散的电荷守恒律以及能量守恒律,最后通过数值实验数据验证该格式的高效性和理论分析的正确性.

英文摘要：

A fourth order compact difference scheme is presented to solve the one-dimensional Schrdinger equation and the method is generalized to solve to the two-dimensional Schrdinger equation.The P-R alternating direction implicit（ADI） technique is implemented for the time discretization.The scheme is not only time saving with high accuracy,but also unconditionally stable.Moreover,it is proved that the scheme preserves discrete conservation laws.Detailed numerical results suggest that the scheme is efficient and consistent with our theoretical analysis.