提出一种交替方向Legendre谱元格式求解二维Schrodinger方程,并对于线性情形给出最优H¹误差估计.该方法把二维问题的计算转化成一维问题的求解,并且采用区域分裂法进一步降低问题的规模.该算法可实现高度并行化,并减少存储，通过选择适当的基函数,使得导出的矩阵是带状稀疏的.通过数值算例比较,该方法显示出一定的有效性.

An alternating direction implicit (ADI) Legendre spectral element method for the two dimensional Schrodinger equation is developed, and the optimal H¹ error estimate for the linear case is given. This method converts the two dimensional computation to one dimension with domain decomposition so that the size of problem and the storage are reduced. The main advantage of the method is its high degree of parallel computation. By choosing appropriate base functions, strip sparse matrices are derived. Numerical experiments show validity of the method. 