superposition of basis states?

[liorda]

1. The problem statement, all variables and given/known data

consider the state (\frac{1}{2}, \frac{1}{2}, \frac{1}{\sqrt{2}}) in L_z basis. If L_x^2 is measured and the result of 0 is obtained, find the final state after the measurement. How probable is this result?

3. The attempt at a solution

I'm not sure if the state is superposition of the known ground states of L_x in L_z representation. How to find the state of the system after the measurement? And should I sum the probabilities of getting each of that state eigenvalues?

thanks.

[liorda]

any moderator, please move my question to quantum physics forum. thanks.