Consider a quantum system evolving under the time-independent Hamiltonian operator H of the form: H = H 0 + V where H 0 is a Hamiltonian with known eigenstates | m ⟩ ⟩ and corresponding eigenvalues E m , and where V is a small perturbation. Moreover, it is assumed without loss of generality that V is purely off-diagonal in the eigenbasis of H 0 , i.e., ⟨ ⟨ m | V | m ⟩ ⟩ = 0 for all m . Indeed, this situation can always be arranged by absorbing the diagonal elements of V into H 0 , thus modifying its eigenvalues to E m ′ = E m + ⟨ ⟨ m | V | m ⟩ ⟩ .