How to predic the possible values of Lx

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

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