Finding E, L and Lz from wavefunction

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

Also thank you very much for your help
 
Yup, and you're welcome.
 

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