论文标题
基于Schrodinger分解方法的Kramers-Pasternack关系的代数推导
Algebraic derivation of Kramers-Pasternack relations based on the Schrodinger factorization method
论文作者
论文摘要
Kramers-Pasternack关系用于计算所有氢原子的所有径向能量的R（正和负）的力矩。它们由两个代数复发关系组成，一个是积极的力量，另一个用于负面。大多数派生使用Feynman-Hellman定理或蛮力集成来确定第二个反向力矩，这是为负时矩完成复发关系所需的。在这项工作中，我们既展示了如何以代数来得出复发关系，又显示了如何通过代数确定第二个反向力矩，这消除了与汉密尔顿相关的教学混乱相对于角动量量子数L而与汉密尔顿相关相关的教学混乱，以便找到逆第二步。
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.
