标题： 受限氦在拉格朗日网格上 显示英文标题

标题： Confined helium on Lagrange meshes

摘要： 拉格朗日网格方法具有在网格上计算的简单性，并且可以具有变分方法的准确性。 它被应用于研究受限的氦原子。 考虑了两种类型的限制。 在周长坐标中研究了通过势能的软限制。 在不可渗透的球形空腔中的硬限制在一组缩放的周长坐标中进行，其变化区间为[0,1]。 计算了电子之间的能量和平均距离以及电子与氦核之间的平均距离。 使用较小的计算时间获得了11到15位有效数字的高精度。 还计算了作用在受限原子上的压力。 对于半径小于1的球体，它们的相对精度优于$10^{-10}$。 对于半径较大至10的情况，它们逐渐降低到$10^{-3}$，但仍优于文献中的最佳结果。 显示英文摘要

摘要： The Lagrange-mesh method has the simplicity of a calculation on a mesh and can have the accuracy of a variational method. It is applied to the study of a confined helium atom. Two types of confinement are considered. Soft confinements by potentials are studied in perimetric coordinates. Hard confinement in impenetrable spherical cavities is studied in a system of rescaled perimetric coordinates varying in [0,1] intervals. Energies and mean values of the distances between electrons and between an electron and the helium nucleus are calculated. A high accuracy of 11 to 15 significant figures is obtained with small computing times. Pressures acting on the confined atom are also computed. For sphere radii smaller than 1, their relative accuracies are better than $10^{-10}$. For larger radii up to 10, they progressively decrease to $10^{-3}$, still improving the best literature results.