Relativistic free complement method for correctly solving the Dirac equation with the applications to hydrogen isoelectronic atoms
Relativistic free complement method for correctly solving the Dirac equation with the applications to hydrogen isoelectronic atoms
复制标题
正确求解狄拉克方程的相对论自由补法及其在氢等电子原子中的应用
DOI：
10.1007/s00214-011-0899-7
复制
发表时间：
2011
影响因子：
1.7
通讯作者：
H. Nakatsuji
中科院分区：
文献类型：
--
作者：
H. Nakashima;H. Nakatsuji
先前报道的用于求解原子和分子的狄拉克-库仑方程的相对论自由补体（FC）方法的准确性已经在氢等电子原子的应用中得到了严格的检验。由哈密顿量生成的 FC 波函数自动处理大分量和小分量之间的正确关系，即 FC 或 ICI 平衡。将FC方法与逆哈密顿方法相结合，可以帮助安全地获得针对狄拉克-库仑方程的几个特征障碍的正确解。为了确保所获得的波函数的准确性，我们检查了类氢原子与精确波函数的总平方偏差、局部能量恒定性、H平方误差以及能量上限和下限。
The accuracy of the relativistic free complement (FC) method, which was previously reported for solving the Dirac–Coulomb equations of atoms and molecules, has been strictly examined with the applications to hydrogen isoelectronic atoms. The FC wave function grown up by the Hamiltonian automatically takes care of the correct relationship between large and small components, i.e., FC or ICI balance. Combining the FC method with the inverse Hamiltonian method can help to obtain correct solutions safely against to several obstacles characteristic to the Dirac–Coulomb equation. To ensure the exactness of the obtained wave function, we examined the total square deviation from the exact wave function, local energy constancy, H-square error, and energy upper and lower bounds for hydrogen-like atoms.