Q. Mechanics: Spin and position state? Need help?

[sutupidmath]

Homework Statement

The electron in a hydrogen atom occupies the combined spin and position staate

$$R_{12}\left(\sqrt{1/3}Y^0_lX_++\sqrt{2/3}Y^1_1X_-\right)$$

(a) If you measured the orbital angular momentum squared ($$L^2$$), what values might you get, and what is the probability of each?

(b) Same for the z component of the orbital angular momentum ($$L_z$$).

Homework Equations

We know that:
$$L^2\psi=h^2l(l+1)\psi\hspace{2cm} (1)$$

and

$$L_z\psi=hm\psi.$$

The Attempt at a Solution

(a)
So, given (1), i was thinking that the values that we might get are

$$2\sqrt{1/3}h^2, \mbox{ and } 2\sqrt{2/3}h^2.$$

I wasn't sure how to deal with the $$R_{12}.$$

I would appreciate if someone would give me a hint on how to get started.

 

[sutupidmath]

Consider this post CLOSED!

I figured it out!