The two-electron atomic systems. S-states

Abstract A simple Mathematica program for computing the S-state energies and wave functions of two-electron (helium-like) atoms (ions) is presented. The well-known method of projecting the Schrödinger equation onto the finite subspace of basis functions was applied. The basis functions are composed of the exponentials combined with integer powers of the simplest perimetric coordinates. No special subroutines were used, only built-in objects supported by Mathematica. The accuracy of results and computa... Title of program: TwoElAtom-S Catalogue Id: AEFK_v1_0 Nature of problem The Schrödinger equation for atoms (ions) with more than one electron has not been solved analytically. Approximate methods must be applied in order to obtain the wave functions or other physical attributes from quantum mechanical calculations. Versions of this program held in the CPC repository in Mendeley Data AEFK_v1_0; TwoElAtom-S; 10.1016/j.cpc.2009.09.012 This program has been imported from the CPC Program Library held at Queen's University Belfast (1969-2018)

摘要：本文提供了一款用于计算双电子（类氦）原子（离子）S态能量与波函数的简易Mathematica程序。本研究采用将薛定谔方程投影至基函数有限子空间的经典方法，基函数由指数函数与最简周长坐标的整数次幂组合构成。本程序未使用任何自定义子程序，仅依托Mathematica内置对象实现。本研究的结果精度与计算...
程序名称：TwoElAtom-S
目录编号：AEFK_v1_0
问题本质：多电子原子（离子）的薛定谔方程尚无解析解，因此必须借助近似方法，方可从量子力学计算中获取波函数或其他物理属性。
孟德莱数据（Mendeley Data）中CPC程序库收录的版本：AEFK_v1_0；TwoElAtom-S；10.1016/j.cpc.2009.09.012
本程序源自贝尔法斯特女王大学所藏的CPC程序库（1969-2018）

搜集汇总

背景与挑战

背景概述

该数据集是一个用于计算两个电子（类氦）原子或离子S态能量和波函数的Mathematica程序，采用将薛定谔方程投影到有限基函数子空间的方法，基函数由指数函数与周长坐标的整数幂组合而成，无需特殊子程序，仅依赖Mathematica内置对象，旨在解决多电子系统薛定谔方程无解析解的问题。