论文标题
氢原子限制在倒高斯电势内
Hydrogen atom confined inside an inverted-Gaussian potential
论文作者
论文摘要
在这项工作中，我们考虑了限制在可渗透球势内的氢原子。限制电势由深度$ω_0$，宽度$σ$的倒高斯函数描述，以$ r_c $为中心。特别是，该模型已用于研究$ C_ {60} $ Fullerene中的原子。对于角动量的最低值，$ l = 0,1,2 $，使用三种不同的数值方法来计算系统的光谱作为参数（$ω_0，σ，R_C $）的函数：（i）lagrange-mesh方法，（i）（i）（ii）第四阶有限差和（iii）限制元素方法。显示了不少于11个重要数字的混凝土结果。同样，在Lagrange-Mesh方法中，分别提出了相应的本征函数和$ s，p $和$ d $ symmetries的前六个州的$ r $的期望值。我们的准确能量也被视为训练人工神经网络的初始数据。它产生有效的数值插值。目前的数值结果改善并扩展了文献中报告的结果。
In this work, we consider the hydrogen atom confined inside a penetrable spherical potential. The confining potential is described by an inverted-Gaussian function of depth $ω_0$, width $σ$ and centered at $r_c$. In particular, this model has been used to study atoms inside a $C_{60}$ fullerene. For the lowest values of angular momentum $l=0,1,2$, the spectra of the system as a function of the parameters ($ω_0,σ,r_c$) is calculated using three distinct numerical methods: (i) Lagrange-mesh method, (ii) fourth order finite differences and (iii) the finite element method. Concrete results with not less than 11 significant figures are displayed. Also, within the Lagrange-mesh approach the corresponding eigenfunctions and the expectation value of $r$ for the first six states of $s, p$ and $d$ symmetries, respectively, are presented. Our accurate energies are taken as initial data to train an artificial neural network as well. It generates an efficient numerical interpolation. The present numerical results improve and extend those reported in the literature.
