相对论类氢本征态间$r^λ$和$βr^λ$矩阵元的新递推关系
New recursion relations of matrix elements of $r^λ$ and $βr^λ$ between relativistic hydrogenic eigenstates
摘要：
我们确定准确的递归关系，这有助于在狄拉克相对论性类氢本征态之间的径向坐标的权力的矩阵元素的评价。幂$λ$可以是任何复数，只要相应项比$r^{-1}$消失得快，如$r \to \infty$。这些公式允许递归地确定径向幂的任何矩阵元素- $r^λ$或$βr^λ$，$β$是狄拉克矩阵-根据前面的两个连续元素。所得结果在相对论原子计算中是有用的。
英文摘要：
We determine exact recurrence relations which help in the evaluation of matrix elements of powers of the radial coordinate between Dirac relativistic hydrogenic eigenstates. The power $λ$ can be any complex number as long as the corresponding term vanishes faster than $r^{-1}$ as $r \to \infty$. These formulas allow determining recursively any matrix element of radial powers --$r^λ$ or $βr^λ$, $β$ is a Dirac matrix-- in terms of the two previous consecutive elements. The results are useful in relativistic atomic calculations.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
