Pauli-Principle Restriction on the Two Matrix of Bopp for Atomic Ground States

L. J. Kijewski, Jerome Percus

Research output: Contribution to journalArticle

Abstract

A lower bound to the ground-state energy of an atom is formulated, using the pair density matrix Γ(2). The major problem in the development of such methods is that of finding necessary conditions on Γ(2) not satisfied by the current optimal class of density matrices. It is shown that the Bopp two-matrix ansatz suffers mainly from the Pauli principle not being satisfied. With the aid of an extensive set of system-dependent identities for Γ(2), numerical computations indicate how energy improvement will follow from insistence on the Pauli principle. A new necessary condition is conjectured which combines the Pauli condition on Γ(1) with a maximum eigenvalue condition on Γ(2).

Original languageEnglish (US)
Pages (from-to)45-54
Number of pages10
JournalPhysical Review
Volume179
Issue number1
DOIs
StatePublished - 1969

Fingerprint

constrictions
ground state
matrices
eigenvalues
energy
atoms

ASJC Scopus subject areas

  • Physics and Astronomy(all)

Cite this

Pauli-Principle Restriction on the Two Matrix of Bopp for Atomic Ground States. / Kijewski, L. J.; Percus, Jerome.

In: Physical Review, Vol. 179, No. 1, 1969, p. 45-54.

Research output: Contribution to journalArticle

Kijewski, L. J. ; Percus, Jerome. / Pauli-Principle Restriction on the Two Matrix of Bopp for Atomic Ground States. In: Physical Review. 1969 ; Vol. 179, No. 1. pp. 45-54.
@article{fac0fe5649224973a11fd7f8c8de0ace,
title = "Pauli-Principle Restriction on the Two Matrix of Bopp for Atomic Ground States",
abstract = "A lower bound to the ground-state energy of an atom is formulated, using the pair density matrix Γ(2). The major problem in the development of such methods is that of finding necessary conditions on Γ(2) not satisfied by the current optimal class of density matrices. It is shown that the Bopp two-matrix ansatz suffers mainly from the Pauli principle not being satisfied. With the aid of an extensive set of system-dependent identities for Γ(2), numerical computations indicate how energy improvement will follow from insistence on the Pauli principle. A new necessary condition is conjectured which combines the Pauli condition on Γ(1) with a maximum eigenvalue condition on Γ(2).",
author = "Kijewski, {L. J.} and Jerome Percus",
year = "1969",
doi = "10.1103/PhysRev.179.45",
language = "English (US)",
volume = "179",
pages = "45--54",
journal = "Physical Review",
issn = "0031-899X",
publisher = "American Institute of Physics Publising LLC",
number = "1",

}

TY - JOUR

T1 - Pauli-Principle Restriction on the Two Matrix of Bopp for Atomic Ground States

AU - Kijewski, L. J.

AU - Percus, Jerome

PY - 1969

Y1 - 1969

N2 - A lower bound to the ground-state energy of an atom is formulated, using the pair density matrix Γ(2). The major problem in the development of such methods is that of finding necessary conditions on Γ(2) not satisfied by the current optimal class of density matrices. It is shown that the Bopp two-matrix ansatz suffers mainly from the Pauli principle not being satisfied. With the aid of an extensive set of system-dependent identities for Γ(2), numerical computations indicate how energy improvement will follow from insistence on the Pauli principle. A new necessary condition is conjectured which combines the Pauli condition on Γ(1) with a maximum eigenvalue condition on Γ(2).

AB - A lower bound to the ground-state energy of an atom is formulated, using the pair density matrix Γ(2). The major problem in the development of such methods is that of finding necessary conditions on Γ(2) not satisfied by the current optimal class of density matrices. It is shown that the Bopp two-matrix ansatz suffers mainly from the Pauli principle not being satisfied. With the aid of an extensive set of system-dependent identities for Γ(2), numerical computations indicate how energy improvement will follow from insistence on the Pauli principle. A new necessary condition is conjectured which combines the Pauli condition on Γ(1) with a maximum eigenvalue condition on Γ(2).

UR - http://www.scopus.com/inward/record.url?scp=0040703640&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0040703640&partnerID=8YFLogxK

U2 - 10.1103/PhysRev.179.45

DO - 10.1103/PhysRev.179.45

M3 - Article

VL - 179

SP - 45

EP - 54

JO - Physical Review

JF - Physical Review

SN - 0031-899X

IS - 1

ER -