论文标题
Hartree-fock能量功能的临界值数量小于常数小于第一个能量阈值的常数
Finiteness of the number of critical values of the Hartree-Fock energy functional less than a constant smaller than the first energy threshold
论文作者
论文摘要
我们研究了Hartree-fock方程和在许多电子问题中普遍使用的Hartree-Fock Energy功能。我们证明，Hartree-fock能量功能的所有临界值的集合小于小于第一个能阈值的常数是有限的。由于是相应的Euler-Lagrange方程的Hartree-fock方程是一个非线性特征值问题的系统，因此线性操作员的光谱理论不适用。目前的结果是获得了与轨道能相关的临界值的有限性，而轨道能小于负常数，并将结果与Koopmans众所周知的定理相结合。主要成分是溶液收敛的证明，以及对限制点功能的Fréchet第二个衍生物的分析。
We study the Hartree-Fock equation and the Hartree-Fock energy functional universally used in many-electron problems. We prove that the set of all critical values of the Hartree-Fock energy functional less than a constant smaller than the first energy threshold is finite. Since the Hartree-Fock equation which is the corresponding Euler-Lagrange equation is a system of nonlinear eigenvalue problems, the spectral theory for linear operators is not applicable. The present result is obtained establishing the finiteness of the critical values associated with orbital energies less than a negative constant and combining the result with the Koopmans' well-known theorem. The main ingredients are the proof of convergence of the solutions and the analysis of the Fréchet second derivative of the functional at the limit point.
