Rayleigh-Ritz variational principle for ensembles of fractionally occupied states

E. K.U. Gross; L. N. Oliveira; W. Kohn

doi:10.1103/PhysRevA.37.2805

Rayleigh-Ritz variational principle for ensembles of fractionally occupied states

E. K.U. Gross^*, L. N. Oliveira, W. Kohn

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

306 Scopus citations

Abstract

The Rayleigh-Ritz minimization principle is generalized to ensembles of unequally weighted states. Given the M lowest eigenvalues E1E2...EM of a Hamiltonian H, and given M real numbers w1w2...wM>0, an upper bound for the weighted sum w1E1 +w2E2+...+wMEM is established. Particular cases are the ground-state Rayleigh-Ritz principle (M=1) and the variational principle for equiensembles (w1=w2=...=wM). Applications of the generalized principle are discussed.

Original language	English
Pages (from-to)	2805-2808
Number of pages	4
Journal	Physical Review A
Volume	37
Issue number	8
DOIs	https://doi.org/10.1103/PhysRevA.37.2805
State	Published - 1988
Externally published	Yes

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title = "Rayleigh-Ritz variational principle for ensembles of fractionally occupied states",

abstract = "The Rayleigh-Ritz minimization principle is generalized to ensembles of unequally weighted states. Given the M lowest eigenvalues E1E2...EM of a Hamiltonian H, and given M real numbers w1w2...wM>0, an upper bound for the weighted sum w1E1 +w2E2+...+wMEM is established. Particular cases are the ground-state Rayleigh-Ritz principle (M=1) and the variational principle for equiensembles (w1=w2=...=wM). Applications of the generalized principle are discussed.",

author = "Gross, {E. K.U.} and Oliveira, {L. N.} and W. Kohn",

year = "1988",

doi = "10.1103/PhysRevA.37.2805",

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AU - Oliveira, L. N.

AU - Kohn, W.

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AB - The Rayleigh-Ritz minimization principle is generalized to ensembles of unequally weighted states. Given the M lowest eigenvalues E1E2...EM of a Hamiltonian H, and given M real numbers w1w2...wM>0, an upper bound for the weighted sum w1E1 +w2E2+...+wMEM is established. Particular cases are the ground-state Rayleigh-Ritz principle (M=1) and the variational principle for equiensembles (w1=w2=...=wM). Applications of the generalized principle are discussed.

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Rayleigh-Ritz variational principle for ensembles of fractionally occupied states

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