粒子自旋4阶辛格式计算误差研究  

The Error in Solving Schrdinger Equation of Wave Function of Particle Spin with 4-order Symposium

作　　者：牟其善[1] 李娟[1] 刘玉真[1] 

机构地区：[1]山东教育学院物理系,山东济南250013

出　　处：《山东科学》2007年第6期45-50,共6页Shandong Science

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.研究了4阶辛差分格式计算结果的误差,并与2阶辛差分格式的结果进行了比较.利用4阶辛格式计算波函数实部和虚部结果的精密度比2阶格式高出7个数量级,即绝对误差低7个数量级,但二者演变规律基本相同,即绝对误差随着时间的推演均周期性地在正数和负数之间来回变动,变化方式类似于正弦、余弦函数,其振幅不断增大.4阶辛格式结果误差的变化图形较2阶辛格式略微滞后.2阶的绝对误差随时间的变化恰好与波函数本身的时间变化率成正比,即波函数绝对误差与其时间变化率的比值随时间的变化呈严格的直线图像,而4阶辛格式结果没有这样的关系.但若考虑到4阶绝对误差在时间上的滞后,也能够变换出类似的直线关系.The numerical solution of wave function is obtained by solving schrǒdinger equation of partical spin with symposium. We investigated the error in the solution of 4-order symposium, which was compared with that of 2-order symposium. The precision of the solution of wave function with 4-order symposium is 7 quantitative ranks higher than that with 2-order symposium, namely its absolute error7 quantitative ranks lower than that of 2-order symposium. However, their error changes are similar, all of which oscillate periodically between positive and negative numbers, and are similar to those of sine or cosine function, while the amplitudes increasing continuously. The changeable error graph of 4-order symposium slightly delays that of 2-order symposium. It is discovered that the absolute error of 2-order symposium of wave function is exactly proportional to the rate of time change of the wave function. In other words, the ratior of the absolute error of a wave function to the rate of its time change is linear,while it is not true for 4-order symposiom. However, considering the delay of 4-order absolute error, we can also obstain similar linear results.

关 键 词：4阶辛格式 自旋 薛定谔方程 波函数 绝对误差 

分 类 号：O411.2[理学—理论物理] TP399[理学—物理]