1. The problem statement, all variables and given/known data The eigenstates of two commuting operators A and B are denoted |a,b> and satisfy the eigenvalue equations A|a,b>=a|a,b> and B|a,b>=b|a,b>. A system is set up in the state |psi> = N(|1,2> + |2,2> + |1,3>) What is the value of the normalization constant N? A measurement of the value of A yields the result 1. What is the probability of this happening? What is the new state |psi'> of the system? 2. Relevant equations None? 3. The attempt at a solution So I did <psi|psi>=1 and got N=sqrt(1/3) Then I thought that a measurement of A is a measurement of it's eigenvalue, so I need the probability of the system being in a state |1,b>. I think the constants in front of an eigenstate here is the amplitude of the system being in a state |a,b> (i.e. the amplitude that a measurement of A will yield a result a). So the total amplitude of measuring a=1 is 2*sqrt(1/3). However this gives a probability of 4/3!!