用松弛法解薛定谔方程

求解定态薛定谔方程常常会涉及到常微分方程的本征值问题.目前解常微分方程本征值用的比较多的方法是以龙格-库塔方法为基础的打靶方法.打靶方法常用,但是计算时间长.当边界条件比较复杂或比较敏感的时候,用松弛法会有更好的效果.本文用松弛法解薛定谔方程,并和理论解进行比较.发现松弛法得到的数值解和理论解符合度很高,而且使用松弛法能够很快得到符合要求的解.

Solving the Schrodinger equation with the relaxation method

The most common method to solve ordinary differential equations is the shooting method based on Runge Kutta method.The shooting method is commonly used,but the calculation time is long.When the boundary conditions are more complex or more sensitive,the relaxation method is better.In this paper,the Schrodinger equation is solved by the relaxation method and compared with the analytical solution.It is found that the numerical solution obtained by relaxation method is in good agreement with the analytical solution,and the accurate solution can be obtained quickly by relaxation method.