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 journalArticlepeer-review

297 Scopus citations


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 languageAmerican English
Pages (from-to)2805-2808
Number of pages4
JournalPhysical Review A
Issue number8
StatePublished - 1988
Externally publishedYes


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