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Orbital Angular Momentum

  1. Mar 13, 2007 #1
    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
     
  2. jcsd
  3. Mar 14, 2007 #2

    dextercioby

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    What is a 3px state ? What quantum numbers does it have ?
     
  4. Mar 14, 2007 #3
    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
     
  5. Mar 14, 2007 #4

    dextercioby

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    As far as i know, the p_x orbital has a definite value of "m_l". So your last answer is wrong.
     
  6. Mar 14, 2007 #5

    Galileo

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    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).
     
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