粒子自旋薛定谔方程辛算法解的相对误差研究  

The Relative Error on Solving Schrdinger Equation of Wave Function of Particle Spin with Symposium

作　　者：牟其善[1] 李树金[2] 李娟[1] 刘玉真[1] 高慧[1] 

机构地区：[1]山东教育学院物理系,山东济南250013 [2]山东教育学院计算机系,山东济南250013

出　　处：《山东教育学院学报》2007年第4期53-56,共4页Journal of Shandong Education Institute

摘　　要：利用辛算法求解粒子自旋问题的薛定谔方程,得到波函数的数值解,对于计算结果的相对误差进行了较为详细的研究与分析。发现波函数的实部和虚部的相对误差周期性地在正数和负数之间来回变动,它们之间有类似于不确定关系的特点:一个相对误差趋向于无穷小时另一个相对误差趋向于无穷大,两者的乘积为一稳定的小负数。随着时间的推进这一乘积按抛物线规律增大。这种误差变化的规律性可以由误差理论给出基本解释。　The Schrdinger Equation of particle spin is solved with symposium,and the numeral solution of wave function is got.It is presented that the relative error analysis of solution in detail.The relative errors of real number part and imaginary number part of wave function change periodically between positive and negative numbers.The relation between the relative error of real number part and that of imaginary number part of wave function is similar to the characteristic of Uncertainty Principle.When one relative error approaches infinitely small,the another one approaches infinitely great.The product of the two relative errors is a small fixed negative number,and it changes as parabola with the passage of time slowly.The regularity of error change can be explained with error analysis theory elementarily.

关 键 词：辛算法 自旋 薛定谔方程 波函数 绝对误差 相对误差 

分 类 号：O411.2[理学—理论物理] TP399[理学—物理]