Solution of the radial equation for hydrogen by the Laplace transform method
Solution of the radial equation for hydrogen by the Laplace transform method
复制标题
拉普拉斯变换法求解氢的径向方程
DOI：
10.1080/0020739880190504
复制
发表时间：
1988
影响因子：
0.9
通讯作者：
J. Shertzer
中科院分区：
文献类型：
--
作者：
J. Shertzer
用拉普拉斯变换法求解氢原子的径向方程。求解径向方程的标准方法需要特别考虑函数的渐近形式和相关的拉盖尔多项式的使用。变换后的径向方程可以用在整个范围内有效的简单级数展开来处理。求和极限由量子数的大小决定，级数的系数得到了一个简单的递推关系.解的逆变换产生精确的径向函数。
The radial equation for the hydrogen atom is solved by the method of Laplace transformation. The standard approach for solving the radial equation requires special consideration of the asymptotic form of the function and the use of the associated Laguerre polynomials. The transformed radial equation can be treated with a simple series expansion valid over the entire range. The summation limits are determined by the values of the quantum numbers nand I.A simple recursion relation is obtained for the coefficients of the series. Inverse transformation of the solution yields the exact radial functions.