氦原子1s2p态的有限元近似能量  

Approximate Energies of the 1s2p-state of Helium by the Finite Element Method

作　　者：郑伟英[1] 应隆安[2] 

机构地区：[1]中科院计算数学研究所,北京100080 [2]北京大学数学科学学院,北京100871

出　　处：《计算物理》2003年第2期119-122,共4页Chinese Journal of Computational Physics

基　　金：国家重点基础研究基金(G1999032803);高等学校博士学科点专项科研基金(99000119)资助项目

摘　　要：　用有限元方法近似计算了1s2p态氦原子单态和三重态的能量,所得结果的相对误差:三重态为10-6,单态为10-4.这一结果比Schertzer[1]对基态氦原子的相应结果稍好.有限元法导致的大型广义矩阵特征值问题,对于基态是对称的,而对于1s2p态是非对称的,给求解带来了难度.由波函数的图形说明,在有界区域上求Schr dinger方程的近似解是合理的.The finite element method is used to obtain numerical solutions of the Schrdinger equation for the Helium 1s2p\|state. The relative errors of approximate energies are 10-6 for triplet and 10-4 for singlet which are slightly smaller than J. Shertzer's results for the Helium ground state \. The generalized eigenvalue problems obtained by FEM are symmetric for the ground state but unsymmetric for 1s2p\|state. It becomes more difficult to solve the problems. Form the graphs of wave functions, it can be seen that it is reasonable to solve the Schrdinger equations in bounded domains.

关 键 词：有限元方法 Hylleraas-Breit变换 SCHROEDINGER方程 

分 类 号：O562.1[理学—原子与分子物理]