Finding E, L and Lz from wavefunction

[the riddick25]

Homework Statement

We were given the wavefunction for a hydrogen atom (ignoring spin) as shown in the link below
We are asked to find the probability of obtaining E=E1, L^2=2 hbar^2 and Lz=hbar

Homework Equations

http://s633.photobucket.com/albums/uu58/john_sharkey/?action=view&current=equation.jpg

The Attempt at a Solution

i have no idea what equations i would need to find the probabilities of finding these results.
If somebody could point me in the right direction it would be much appreciated.

 

[ideasrule]

That wavefunction is a superposition of two stationary states, namely psi_100 and psi_211. Each stationary state has a definite E, L^2, and Lz: if you know that a particle is in the state psi_100, for example, you will always get E1 when you measure its energy.

This particle is not yet in any state, but when you take a measurement, it randomly collapses into one of the two stationary states. The question is essentially asking what the probability of it collapsing into the state with energy E1 is, and ditto for L^2 and Lz.

 

[the riddick25]

is the probability of obtaining each stationary state just 2/3 and 1/3 respectively?

Also thank you very much for your help

 

[ideasrule]

Yup, and you're welcome.