Kramers-Pasternack关系的Schrodinger分解代数推导
Algebraic derivation of Kramers-Pasternack relations based on the Schrodinger factorization method
摘要：
Kramers-Pasternack关系用于计算类氢原子所有径向能量本征函数的r矩（正的和负的）。它们由两个代数递归关系组成，一个用于正幂，一个用于负幂。大多数推导采用Feynman-Hellman定理或蛮力积分来确定第二逆矩，这是完成负矩递推关系所需的。在这项工作中，我们展示了如何推导递归关系代数和如何确定第二个逆矩代数，这消除了教学上的混乱与微分哈密顿相对于角动量量子数l，以找到逆二阶矩。
英文摘要：
The Kramers-Pasternack relations are used to compute the moments of r (both positive and negative) for all radial energy eigenfunctions of hydrogenic atoms. They consist of two algebraic recurrence relations, one for positive powers and one for negative. Most derivations employ the Feynman-Hellman theorem or a brute-force integration to determine the second inverse moment, which is needed to complete the recurrence relations for negative moments. In this work, we show both how to derive the recurrence relations algebraically and how to determine the second inverse moment algebraically, which removes the pedagogical confusion associated with differentiating the Hamiltonian with respect to the angular momentum quantum number l in order to find the inverse second moment.
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。
