What Do Expectation Values Tell Us About Quantum State Probabilities?

[jaobyccdee]

In measuring the x component of angular momentum of a state, by using the expectation value calculation of Lx, i got i/3 h bar - i/3 h bar, does this means that the probability of h bar is i/3 and the probability of 0 h bar is 0 and the probability of -h bar is i/3? If so, when is the probability of 0 h bar not 0?

 

[vela]

No, expectation values tell you nothing about the individual probabilities. Also, probabilities are real numbers between 0 and 1. It makes absolutely no sense to talk of a probability of i/3.