How to predic the possible values of Lx

[EliotHijano]

Hello, I would like to ask you something about angular momentum in quantum mechanics;
If I know that when t=0, my wave function is $$\Psi=\Upsilon^{m}_{l}$$ and $$l=3$$ and $$m=0$$, How can I calculate the probability of getting the value $$\hbar$$ meassuring $$L_{x}$$?

 

[Count Iblis]

Why not perform a passive rotation of 90° around the y-axis. Under this rotation, the |3,m> states transform to the |3,m> states in the x-basis. But you get them expressed in terms of the z-basis. So, you then see how |3,1> in the x-basis is expressed in terms of the |3,m> states in the z-basis and you can then read-off the inner product.

 

[EliotHijano]

Thank you Count Iblis, that was the answer, I did it before reading this, but thank you anyway!
the answer was 3/16 If i remember correctly.

 

[EliotHijano]

Maybe it is usefull for anybody to see the process. Look at the pdf.