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I have a quick homework problem because I am confused. So a wave function with l = 1 in the state:

[tex] |\psi> = \frac{1}{\sqrt{14}} \[ \left( \begin{array}{ccc}

1 \\

2 \\

3i \end{array} \right)\] [/tex]

and i have to find the probability to be in state [tex] \hbar, -\hbar, 0 [/tex] in [tex] L_z [/tex], so i applied [tex] L_z [/tex] so [tex] |\psi> [/tex] and got

[tex] L_z|\psi> = \frac{\hbar}{\sqrt{14}} \[ \left( \begin{array}{ccc}

1 \\

0 \\

-3i \end{array} \right)\] [/tex]

How do i find the probabilities from that?

Thanks,

Biest