球面调和函数的代数构造
Algebraic construction of spherical harmonics
摘要：
众所周知，氢原子的角波函数是球谐函数，并且作为偏微分方程的解而获得。而微分算子由$SU(2)$代数的Casimir算子给出，其特征值$l(l+1) \hbar^2$（其中$l$为非负整数）可以用代数方法很容易地求出.因此，波函数的形状也可以通过扩展代数方法来获得。在本文中，我们描述的方法，并表明，具有不同的量子数的波函数连接的情况下，$l=0$，1和2的旋转群。
英文摘要：
The angular wave functions for a hydrogen atom are well known to be spherical harmonics, and are obtained as the solutions of a partial differential equation. However, the differential operator is given by the Casimir operator of the $SU(2)$ algebra and its eigenvalue $l(l+1) \hbar^2$, where $l$ is non-negative integer, is easily obtained by an algebraic method. Therefore the shape of the wave function may also be obtained by extending the algebraic method. In this paper, we describe the method and show that wave functions with different quantum numbers are connected by a rotational group in the cases of $l=0$, 1 and 2.
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。
