What is L^2Ψ for a 3px state of a H-atom?

[mordacious]

Awesome forum here!

I'm stuck on a homework problem and need some guidance.

A H-atom exists in a 3px state. What would be the result of measuring the total orbital angular momentum of this state (e.g. 100 measurements)?

I assume when they say 100 measurements that they mean the expectation value? If so there is now the problem of which wavefunction to use as a 3px state has three due to m = -1, 0, +1. I remember something about how orbitals in the same subshell can be combined but I can't find it in my notes and I'm not sure if this is what I'm looking for.

Anyways, even if I just choose one randomly, finding ∫Ψ*L^2Ψdτ is a huge task.

Am I just going about this all wrong?

Thanks,
Ashley

 

[dextercioby]

What is a 3px state ? What quantum numbers does it have ?

 

[mordacious]

What is a 3px state ? What quantum numbers does it have ?

n = 3
l = 1
m = -1, 0, +1

I'm starting to think this is more of a thinking question than a calculation question. If 3p-1 and 3p+1 give one value and 3p0 gives 0 then over 100 measurements the average value would be 0. Does this sound logical?

Ashley

 

[dextercioby]

As far as i know, the p_x orbital has a definite value of "m_l". So your last answer is wrong.

 

[Galileo]

It wouldn't matter if the eigenvalues of L^2 don't depend on m. So do they?

Doing the integral looks like a fun exercise, but it's not necessary. What is L^2Ψ? (Hint: H and L^2 commute for the H-atom).