1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    blue_leaf77

    User Avatar
    Science Advisor
    Homework Helper

    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.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Commuting observables
  1. Commuting observables (Replies: 2)

Loading...