一维无限深势阱的辛算法解分析  

The Solution Analysis on Solving the Equation of Rectangular Potential Well with Symposium

作　　者：牟其善[1] 王建国[1] 

机构地区：[1]山东教育学院数理系,山东济南250013

出　　处：《山东教育学院学报》2003年第4期65-68,共4页Journal of Shandong Education Institute

摘　　要：利用辛算法计算一维无限深势阱的含时薛定谔方程,解得的波函数的图象与其绝对误差的图象完全相似,这说明各点的相对误差趋向于一个固定值。经计算相对误差在各个x格点处完全相同。波函数相对误差随时间的演变表现出一定的规律性,其实数部分和虚数部分的相对误差周期性地在正负之间来回变化。波函数的实数部分和虚数部分的相对误差之间有类似于测不准原理的关系,一个相对误差趋向于极小时另一个相对误差趋向于极大,两者的乘积为一稳定的小数,随着时间的推进这一小数的绝对值缓慢增大。The Schrodinger Equation of rectangular potential well is solved with symposium. The graph of wave function and the one of its absolute errors are alike perfectly. It is illustrated that the relative errors of wave function in different X points approach a fixed value at the same time. This is verified with calculation. It is uncovered that varying regularity of relative errors of wave function with the passage of time. 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 the one of imaginary number part of wave function is similar to the Uncertainty Principle. When one relative error approaches infinitely small, the another one approaches infinitely great. The product both relative errors is a fixed small number. The absolute value of the small number increases with the passage of time slowly.

关 键 词：辛算法 一维无限深势阱 薛定谔方程 波函数 相时误差 误差分析 

分 类 号：D174[政治法律—政治学]