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International Journal of Quantum Chemistry

About the relationship between some necessary conditions for N‐representability

H. Kummer

Published Dec 1, 1977• 18 citations
Publisher

Abstract

Abstract The relationship between well known necessary conditions for N‐representability of the reduced two‐density matrix is investigated. It is shown that the G‐condition implies two conditions of the operator endomorphism type: the C‐ and the B‐condition.
DOI
10.1002/qua.560120606

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Given the set 𝒮N of all operator endomorphisms T with the property that whenever D is any 2-density operator, then T (D) is N-representable is considered. We specify a pair {Q2,PN} of extreme points of 𝒮N which are related to each other via the particle-hole duality (Theorem 1.2). The rest of the paper is devoted to a complete characterization of the set ŜN of all operator endomorphisms T with the property that whenever D is any 2-density operator then T (D) is quasi-N-representable, i.e., satisfies the necessary conditions Id, QN, BN, and CN.
Properties and NNN-representability conditions of the two-body density matrix
A summary is presented of the properties of the coefficient matrices formed by expanding the two-body reduced density matrix in a complete set of two-electron wave functions. Calculating the relationship between the many electron wave function and these so-called two-body density matrices enables the derivation of necessary NNN-representability conditions that ensure a given matrix obeys the postulates of many-body quantum mechanics.