哈特里福克能量泛函的临界值的有限个数小于一个常数,小于第一个能量阈值

IF 0.6 4区 数学 Q3 MATHEMATICS
Sohei Ashida
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引用次数: 3

摘要

研究了在许多电子问题中普遍使用的Hartree-Fock方程和Hartree-Fock能量泛函。证明了Hartree-Fock能量泛函的所有临界值小于小于第一个能量阈值的常数的集合是有限的。由于Hartree-Fock方程即相应的Euler-Lagrange方程是一个非线性特征值问题系统,因此线性算子的谱理论不适用。本文通过建立轨道能量小于负常数的临界值的有限性,并结合著名的库普曼定理,得到了目前的结果。主要内容是证明解的收敛性和分析泛函在极限点处的二阶导数。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
FINITENESS OF THE NUMBER OF CRITICAL VALUES OF THE HARTREE-FOCK ENERGY FUNCTIONAL LESS THAN A CONSTANT SMALLER THAN THE FIRST ENERGY THRESHOLD
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 Fr\'echet second derivative of the functional at the limit point.
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来源期刊
CiteScore
0.80
自引率
0.00%
发文量
10
审稿时长
>12 weeks
期刊介绍: The Kyushu Journal of Mathematics is an academic journal in mathematics, published by the Faculty of Mathematics at Kyushu University since 1941. It publishes selected research papers in pure and applied mathematics. One volume, published each year, consists of two issues, approximately 20 articles and 400 pages in total. More than 500 copies of the journal are distributed through exchange contracts between mathematical journals, and available at many universities, institutes and libraries around the world. The on-line version of the journal is published at "Jstage" (an aggregator for e-journals), where all the articles published by the journal since 1995 are accessible freely through the Internet.
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