1. The problem statement, all variables and given/known data Suppose that a Hermitian operator A, representing measurable a, has eigenvectors |A1>, |A2>, and |A3> such that A|Ak> = ak|Ak>. The system is at state: |psi> = ((3)^(-1/2))|A1> + 2((3)^(-1/2))|A2> + ((5/3)^(1/2))|A3>. Provide the possible measured values of a and corresponding probabilities. 2. Relevant equations (A)(psi) = sum[anCnPsin] 3. The attempt at a solution It would seem that A1 = (3)^(-1/2), A2 = 2((3)^(-1/2), and A3 = (5/3)^(1/2), but the state is not normalized so the probabilities don't add up to one... so I am confused about how to handle this.