Two-level variational contamination estimate (source code)

= Two-level variational contamination estimate
{title2=$|c_b/c_a|^2\simeq(\widetilde E-E_a)/(E_b-\widetilde E)$}

If a trial <quantum state> is dominated by two <energy eigenstates> of distinct <energies> $E_a<E_b$, then its <Rayleigh quotient> is approximately their probability-weighted mean. Rearranging that mean gives the displayed relative admixture. Neglected states must make small contributions to the energy numerator as well as to <wavefunction normalization>; small probabilities alone need not suffice if their energies are large.