Using bra-ket notation, consider a given system that begins in a state | ψ ψ ⟩ ⟩ , and an observable operator O ^ ^ with the set of eigenstates { | ω ω i ⟩ ⟩ } each with a corresponding eigenvalue λ λ i . A measurement of O ^ ^ is made, and the probability of getting λ λ i is as follows: