I am working through this quantum mechanics homework question and I am a little confused on what I am being asked to do. I have come to one of two possible answers but I don't think either is correct.
Say you have a ket $\psi$ I am asked to find the possible outcomes of measuring the observable values of the operators given in the problem.
I have already shown that they are Hermitian. But I am not sure if I am supposed to calculate the expected values of the operator $\Omega$. where the expecred value is found by $<\Omega> = <\psi|\Omega|\psi>$ I don't think this is correct because the problem asks for the outcomes of measuring the obersvables.
So then I thought maybe because I diagonalized $\Omega$ all I need to do is show that the observables are the eigenvalues of the operator? Which are just down the diagonal of $\Omega$. But again I am suspicious of this because then I am asked to find the probability of each of the observables and I am not sure how to do that with just knowing that they are observable. Don't I need like an observation state ket or something like that? Something that would go in the equation: $P(\omega)= |<\psi|\omega>|^2$ I tried to find some stuff online but some of the online solutions seem to do the reverse order for $\psi$ and $\omega$ to find the probability.
Which of these methods is correct to measure the observables? Or am I completely off?