摘要
通过谐振子实例揭示了利用辛算法求解薛定谔方程所得波函数的相对误差变化的规律性 .通过计算发现任一时刻波函数在各个x格点处的相对误差完全相同 .波函数实数部分和虚数部分的相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 ,其周期为 62 8步或说是πs .波函数的实数部分和虚数部分的相对误差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数 .
The varying regularity of relative errors of wave function is uncover ed while the Schrodinger equation of harmonic oscillator is solved with symposiu m. It has been found through calculation that relative errors of wave function i n different X points are all the same a t the same time. The relative errors of real number part and imaginary number pa rt of wave function change periodically between positive and negative numbers wi th the passage of time. The period is 628 steps or π seconds. The relation betw een the relative error of real number part and the one of imaginary number part of wave function is similar to the characteristic of Uncertainty Principle. Whe n one relative error approaches infinitely small, the another one approaches inf initely great. The product of the two relative errors is a fixed small number. T he absolute value of the small number increases with the passage of time slowly.
出处
《山东大学学报（工学版）》
CAS
2004年第1期120-124,共5页
Journal of Shandong University（Engineering Science）
关键词
辛算法
谐振子
薛定谔方程
波函数
相对误差
误差分析
symposium
harmonic oscillator
Schrodinger equa tion
wave function
relative error
error analysis
