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 | |
| State | Published - 1988 |
| Externally published | Yes |