Possible measurement, eigenvalues of eigenfunctions and probabilities

[unscientific]

Homework Statement

Suppose the angular wavefunction is $\propto (\sqrt{2} cos(\theta) + sin (\theta) e^{-i\phi} - sin (\theta) e^{i\phi})$, find possible results of measurement of:

(a) $\hat {L^2}$
(b)$\hat {L_z}$

and their respective probabilities.

Homework Equations

The Attempt at a Solution

Part (a)
Eigenvalue is $2\hbar^2$. Thus that is the possible result. How do I find the probability of that outcome?

 

[strangerep]

Ahem. I think you could put more than <nothing> in your "relevant equations" section. E.g., what are explicit expressions for your operators in this case? You could also write the general formula for computing a probability for a particular observable and a given state. You could also show some detail of how you arrived at the eigenvalue for $\hat L^2$.

It also wouldn't hurt to state the source of your question.

Bear in mind that if you're unwilling to put more effort into your post, then why should others put effort into helping you?