## How to apply an algebraic operator expression to a ket found in Dirac’s QM book?

I’ve been trying to learn quantum mechanics from a formal point of view, so I picked up Dirac’s book. In the fourth edition, 33rd page, starting from this:ξ|ξ′⟩=ξ′|ξ′⟩ (Where ξ is a linear operator and all the other ξ′‘s are eigen-(value|ket)s.) ,and this:ϕ(ξ)=a1ξn+a2ξn−1⋯an=0 (where ϕ is an algebraic expression) He has deduced ϕ(ξ)|ξ′⟩=ϕ(ξ′)|ξ′⟩ I understand … Read more