论文标题
Hartree-fock方程的一组解决方案的结构
Structures of sets of solutions to the Hartree-Fock equation
论文作者
论文摘要
Hartree-fock方程是与Hartree-fock Energy功能相对应的Euler-Lagrange方程，用于许多电子问题。由于Hartree-fock方程是一个非线性特征值问题的系统，因此对所有解决方案集合的结构的研究都需要与线性操作员的特征函数集不同的新方法。在本文中，我们证明，与Hartree-fock能量功能的临界值相关的所有解决方案的集合小于第一个能量阈值是有限数量的紧凑型连接的房地产空间的联合。结果也将是研究求解方程的近似方法的基础。
The Hartree-Fock equation which is the Euler-Lagrange equation corresponding to the Hartree-Fock energy functional is used in many-electron problems. Since the Hartree-Fock equation is a system of nonlinear eigenvalue problems, the study of structures of sets of all solutions needs new methods different from that for the set of eigenfunctions of linear operators. In this paper we prove that the sets of all solutions to the Hartree-Fock equation associated with critical values of the Hartree-Fock energy functional less than the first energy threshold are unions of a finite number of compact connected real-analytic spaces. The result would also be a basis for the study of approximation methods to solve the equation.
