Schrdinger方程单内点精细积分法与差分法比较研究

Comparative Study of the One-Point High Pre cise Integration Method and the Finite Difference Methods for Schrdinger Equation

可用单内点子域精细积分法求解Schrdinger方程初值问题。当单内点精细积分中的传递函数即指数函数用Taylor展开式的一阶近似来替代时,精细积分转化为差分方程。文章研究了这一对应关系。各种常见差分格式均找到了对应的单点精细积分格式,并在单点精细积分一般公式中得到了统一表达式。

The initial problem of Schrdinger equation can be s olved by using one-point sub-domain high precise integration method. Whe n the exponential function in this method is replaced by different ex pressions of its approximation, this method is transferred to different finite difference methods. Comparative study of these two methods is m ade in this paper. Different kinds of finite difference method can be expressed in terms of the corresponding approximations of one-point hi gh precise integration method.