Equal-coupling three-state perturbation
= Equal-coupling three-state perturbation
A real perturbation with zero diagonal and every off-diagonal element $t$ has one <eigenvalue> $2t$ on the symmetric <vector> and a twofold <eigenvalue> $-t$ on its <orthogonal complement>. It is $t(J_3-I)$, where $J_3$ is the <all-ones matrix>. Diagonal entries alone do not give first-order energies in a degenerate subspace.