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Citation: Chunpeng Wang, Tianying Yan. Hartree方法求解基态氦原子的电子波函数[J]. University Chemistry, ;2026, 41(8): 420-433. doi: 10.12461/PKU.DXHX202507063 shu

Hartree方法求解基态氦原子的电子波函数

Chunpeng Wang ,
Tianying Yan ^,

School of Materials Science and Engineering, Nankai University, Tianjin 300350, China

Corresponding author: Tianying Yan, tyan@nankai.edu.cn
Received Date: 16 July 2025
Accepted Date: 18 September 2025

求解多电子体系波函数是量子化学教学中的重要问题。本文以基态氦原子为例，使用Hartree方法求解其基态电子轨道及波函数。首先在薛定谔方程的基础上，引入Hartree Product近似多电子体系的波函数，推导出了电子轨道的Hartree方程；其次，引入3-21G基组并通过线性变分法及自洽计算优化基组系数，求解电子轨道；对照相关公式编写计算机程序并计算出结果，以便学生对照理论推导及程序编写。本文可望帮助学生更好地学习与理解多电子体系波函数的推导、基于Hartree方法的平均场近似以及自洽求解方法。
- Hartree product,
- Hartree equation,
- Mean-field approximation,
- 3-21G basis set,
- Self-consistent method
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