氢原子轨道矩阵元的递推关系式

The Recursive Relations in the Matrix Elements of Hydrogen Atomic Orbits

本文使用超维里定理与升降算符方法,导出了氢原子跃迁矩阵元与平均值计算的一些递推关系式.使用这些递推关系式可克服直接计算公式中交替双重求和所带来的计算机舍入误差,可从少数几个低阶矩阵元出发,求出任意幂次径向算符的矩阵元,从而可为里德堡原子激发态结构的现代研究提供必备的高阶微扰计算公式.

Some recursive relations were derived for the radial matrix elements of Hydrogenic Atom using hypervirial Theorem and ladder operators. These relations are very useful in calculating high order matrix elements recursively from a few known values of lower order on.es to a high degree of accuracy without the round error of computation as in the standard formula. The consequence of this paper can be extended to the study of Rydberb states of multi-electron atoms.