论文标题
Hartree-fock方程的SCF序列的收敛
Convergence of SCF sequences for the Hartree-Fock equation
论文作者
论文摘要
Hartree-fock方程是许多电子问题中的基本方程。在量子化学中找到解决方程的解决方案是实际上重要的。自一致的字段（SCF）方法是解决Hartree-fock方程的标准数值计算方法。在本文中，我们证明了SCF过程中获得的函数的序列由一对函数对组成，这些函数在通过适当的单位矩阵乘以后收敛，从而强烈确保SCF方法的有效性。提供了足够的条件，即在乘以单位矩阵后，将极限作为解决方程的解决方案，并证明了相应密度运算符的收敛性。该方法主要基于序列对关键集合的临界功能，紧凑性的方法的证明，以及针对另一个功能近临界点的另一个功能性的不平等现象的证明。
The Hartree-Fock equation is a fundamental equation in many-electron problems. It is of practical importance in quantum chemistry to find solutions to the Hartree-Fock equation. The self-consistent field (SCF) method is a standard numerical calculation method to solve the Hartree-Fock equation. In this paper we prove that the sequence of the functions obtained in the SCF procedure is composed of a sequence of pairs of functions that converges after multiplication by appropriate unitary matrices, which strongly ensures the validity of the SCF method. A sufficient condition for the limit to be a solution to the Hartree-Fock equation after multiplication by a unitary matrix is given, and the convergence of the corresponding density operators is also proved. The method is based mainly on the proof of approach of the sequence to a critical set of a functional, compactness of the critical set, and the proof of the Łojasiewicz inequality for another functional near critical points.
