RS 2nd-order energies for 2-level system with off-diagonal perturbation

Textbook exact check of the RS 2nd-order formula. Take H_0 = diag(0, Δ) and V = v·σ_x = v·[[0,1],[1,0]] (purely off-diagonal, real v > 0). First-order energies vanish: ⟨0|V|0⟩ = ⟨1|V|1⟩ = 0. Second-order: E_0^(2) = |⟨1|V|0⟩|² / (E_0^(0)…