Solution of the radial equation for hydrogen atom: series solution or Laplace transform?
Solution of the radial equation for hydrogen atom: series solution or Laplace transform?
复制标题
氢原子径向方程的解：级数解还是拉普拉斯变换？
DOI：
10.1080/0020739900210609
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发表时间：
1990
影响因子：
0.9
通讯作者：
W. Mei
中科院分区：
文献类型：
--
作者：
Yi;W. Mei
研究了求解氢原子径向方程的不同方法。我们指出了几个重要的问题：在传统的级数求解方法中，当发现指示方程的两个根相差一个整数时，根据已知定理只能有一个独立的解；在 Shertzer 最近采用的拉普拉斯变换方法中，隐含地假设了解的渐近行为。我们追溯了薛定谔最初的处理方法并回顾了他严格的拉普拉斯变换方法。最后，讨论了如何在不同层次上呈现该主题的建议。
Different approaches to the solution of the radial equation for the hydrogen atom are examined. We point out several important issues: In the conventional series solution method, when two roots of the indicial equation are found to differ by an integer, there can be only one independent solution according to the known theorem; in the recent Laplace transform approach adopted by Shertzer, the asymptotic behaviour of the solution was implicitly assumed. We traced back the original treatment of Schrodinger and reviewed his rigorous Laplace transform approach. Finally, the suggestion of how to present this subject at different levels is discussed.