洛仑兹-狄拉克方程的新降阶方法

A New Order Reduction of Lorentz-Dirac Equation

针对洛仑兹-狄拉克方程的新降阶方法在氢原子中的适用尺度问题,通过数值计算二维氢原子来比较新降阶方法和原方法在2费米到100 000费米区间内的差异,两种降阶方法在远离质子的区域计算结果基本一致,而在靠近质子几费米区域内,新方法的结果和原方法相差较大.表明在氢原子外围区域,两种方法对于洛仑兹-狄拉克方程来说都是适用的;研究电子在更近区域内的运动行为,新降阶方法更加准确.新降阶方法计算的表达式比原降阶方法复杂,所以关于氢原子,有时联合使用两种降阶方法也会是一个不错的考量.

This paper describes the applicability of a new order reduction of Lorentz-Dirac equation for a hydrogen atom. It is shown that the new order reduction could be viable on a wider scale in comparison with the original algorithm. By calculating the two-dimensional hydrogen atom, the author figures out that the original method is similar to the results of new order reduction in remote domain of proton and they produce inconsistent results as electron moves close to the proton, which demonstrates that both methods are applicable towards Lorentz-Dirac equation. However, the new order reduction turns out more accurate during the study of electron motion behaviors in much nearer areas. Given the complexity of the order reduction calculations, the joint use of both order reductions for two-dimensional hydrogen atoms tends to be more effective.