变分法和级数法求解M-Fermi方程
Variation and Series Approach to the Thomas-Fermi Equation
摘要：
本文重新考虑了描述重中性原子库仑势屏蔽的托马斯-费米方程.利用变分原理得到了其数值解的精确表达式。所提出的新的解决方案具有更精确的渐近行为在大的距离从原点，并允许我们获得的初始斜率的精确值。所得到的新的变分解也可以在幂级数类似的贝克的，但更精确的，甚至比一些系列的解决方案，最近已经得到的同伦分析方法和修改的变分方法。
英文摘要：
The Thomas - Fermi equation describing the screening of the Coulomb potential inside heavy neutral atoms is reconsidered. An accurate representation for its numerical solution was obtained by means of the variational principle. The proposed new solution has more precise asymptotic behaviour at large distances from the origin and allows us to obtain the exact value of the initial slope. The obtained new variational solution can also be developed in power series similar to the Baker's ones but more precise even than some series solutions that have been recently obtained within the homotopy analysis method and a modified variational method.
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