Our earlier treatment started by denoting the eigenvectors ( 1 0 ) and ( 0 1 ) as the matrix representation of eigenstates | ψ ψ 1 ⟩ ⟩ and | ψ ψ 2 ⟩ ⟩ of a two-state system. Using bra–ket notation the matrix elements of H ′ are actually the terms