By attaining an accuracy of 30 significant figures, in the present work we have calculated the expectation values of $$\langle {r^{ - 2}}\rangle $$ of a few states for the confined hydrogen atom and the confined harmonic oscillator, as a function of the confinement radius $$R_{c}$$. In comparison to other calculations reported in the literature, our results are found to be more accurate. This numerical precision was achieved by using the exact wave function of each system.

中文翻译：

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精确计算径向期望值 $$\varvec{\langle {r^{ - 2}}\rangle }$$ 用于受限氢原子和各向同性谐波振荡器

通过达到 30 位有效数字的精度，在目前的工作中，我们计算了受限氢原子和受限谐振子的几种状态的 $$\lange {r^{ - 2}}\rangle $$ 的期望值，作为限制半径 $$R_{c}$$ 的函数。与文献中报道的其他计算相比，我们发现我们的结果更准确。这种数值精度是通过使用每个系统的精确波函数来实现的。