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Commuting observables

  1. Mar 18, 2016 #1
    1. The problem statement, all variables and given/known data
    A particle is in a state described by a wave function of the form ψ(r) = (x+y+z)f(r).
    What are the values that a measurement of L2 can yield? What is probability for all these results?

    2. Relevant equations

    3. The attempt at a solution
    I feel this problem shouldn't be too hard but I've been struggling with quantum since last semester so any guidance would be nice. I think i should probably write the function in spherical terms to start off with. but I'm not too clear on where to go from there. I also know that i need to use Ylm too but again, I'm pretty confused.
  2. jcsd
  3. Mar 18, 2016 #2


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    It will be helpful to use the spherical harmonics written in Cartesian coordinates. Your task is to find ##Y_{lm}##'s in which the given ##\psi(\mathbf{r})## is expanded, $$\psi(\mathbf{r}) = f(r)\sum_{lm} c_{lm} Y_{lm}(\hat{r})$$
  4. Mar 18, 2016 #3
    ok ill try to do some work with that. I'm still pretty lost on what the whole Ylm thing is about but hopefully i can make some sense of it.
  5. Mar 19, 2016 #4
    I don't know what book you're studying out of, but most go through the steps to show that L2Ψ=ħ2l(l+1)Ψ That might help make the problem a bit easier.
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