Suppose that two operators X and N have the commutation relation [ N , X ] = c X for some scalar c. If | n ⟩ ⟩ is an eigenstate of N with eigenvalue equation N | n ⟩ ⟩ = n | n ⟩ ⟩ , then the operator X acts on | n ⟩ ⟩ in such a way as to shift the eigenvalue by c : N X | n ⟩ ⟩ = ( X N + [ N , X ] ) | n ⟩ ⟩ = X N | n ⟩ ⟩ + [ N , X ] | n ⟩ ⟩ = X n | n ⟩ ⟩ + c X | n ⟩ ⟩ = ( n + c ) X | n ⟩ ⟩ .