氦原子及类氦离子基态的二参数变分法研究

Two-parameter variational approach to the ground state energys of the helium atom and quasi-heliumion

提出了一种计算氦原子及类氦离子基态能量和波函数的二参数变分法,包括试探波函数的设计和基态能量表达式的推导,并用Mathematica 5.0软件的优化计算功能方便快捷地计算出基态能量,将计算结果与实验结果和部分所列文献的结果进行对比.结果表明,本文所得精度较高,变分参数个数较少.同时强调交换对称性和量子态的交缠在双电子原子体系问题中的重要性.

A variational method of two parameters for studing ground state energys and wave functions of the helium atom and quasi-heliumion is proposed. We have designed the tested the wave function and derive the ground level expression by solving the radial Schroedinger equation. The ground energy is evaluated by means of the optimized computation of Mathematica 5.0. Our result is compared with the experimental data and the result of other variational methods. It is shown that our result is much precision and the number of variational parameters is less than that of other methods. Meanwhile the importance of permutation symmetry and entanglement of quantum state in the system of two-electron atom is emphasized.