Nonrelativistic limit of the Dirac-Fock equations

被引：28

作者：

Esteban, MJ ^{[1
]}

Séré, E ^{[1
]}

机构：

[1] Univ Paris 09, CEREMADE, CNRS, UMR 7534, F-75775 Paris 16, France

来源：

ANNALES HENRI POINCARE | 2001年 / 2卷 / 05期

关键词：

D O I：

10.1007/s00023-001-8600-7

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

In this paper, the Hartree-Fock equations are proved to be the non relativistic limit of the Dirac-Fock equations as far as convergence of "stationary states" is concerned. This property is used to derive a meaningful definition of "ground state" energy and "ground state" solutions for the Dirac-Fock model.

引用

页码：941 / 961

页数：21

共 16 条

[1] THERE ARE NO UNFILLED SHELLS IN UNRESTRICTED HARTREE-FOCK THEORY [J].

BACH, V ;

LIEB, EH ;

LOSS, M ;

SOLOVEJ, JP .

PHYSICAL REVIEW LETTERS, 1994, 72 (19) :2981-2983

[2] MINIMAX CHARACTERIZATION OF SOLUTIONS FOR A SEMILINEAR ELLIPTIC EQUATION WITH LACK OF COMPACTNESS [J].

BUFFONI, B ;

JEANJEAN, L .

ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 1993, 10 (04) :377-404

[3] On the evaluation of the norm of an integral operator associated with the stability of one-electron atoms [J].

Burenkov, VI ;

Evans, WD .

PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 1998, 128 :993-1005

[4] Variational characterization for eigenvalues of Dirac operators [J].

Dolbeault, J ;

Esteban, MJ ;

Séré, E .

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2000, 10 (04) :321-347

[5] VARIATIONAL PRINCIPLE [J].

EKELAND, I .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1974, 47 (02) :324-353

[6] Solutions of the Dirac-Fock equations for atoms and molecules [J].

Esteban, MJ ;

Séré, E .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1999, 203 (03) :499-530

[7]

GRIESEMER M, 1999, DOC MATH, V4, P275, DOI [DOI 10.1112/S0024610799007930), DOI 10.4171/DM/61]

[8] SPECTRAL THEORY OF OPERATOR (P2+M2)1/2 - ZE2-R [J].

HERBST, IW .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1977, 53 (03) :285-294

[9] RELATIVISTIC SELF-CONSISTENT-FIELD THEORY FOR CLOSED-SHELL ATOMS [J].

KIM, YK .

PHYSICAL REVIEW, 1967, 154 (01) :17-&

[10] HARTREE-FOCK THEORY FOR COULOMB SYSTEMS [J].

LIEB, EH ;

SIMON, B .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1977, 53 (03) :185-194

← 1 2 →