WLOG, consider a state i=0: the effect of the perturbation will be to modify the state and its corresponding energy slightly; The eigenstate |n0⟩ will become |ϕ0⟩ and ...WLOG, consider a state i=0: the effect of the perturbation will be to modify the state and its corresponding energy slightly; The eigenstate |n0⟩ will become |ϕ0⟩ and E0 will shift to E0+ΔE0, where