How to Find the Final State and Probability After Measuring \(L_x^2\)?

[liorda]

Homework Statement

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?

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.