Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Coupled Angular Momentum sates and probability

  1. Feb 19, 2005 #1
    Two p electrons are in the coupled angular momentum states |lml1l2>=|2,-2,11>. What is the joint probability of finding the two electrons with L1z and L2z?

    Here is my thinking,

    With m1 + m2 =-2, the expansion becomes

    |2,-2,11>= C0-2|1,0>1|1,-2>2 + C-20|1,-2>1|1,0>2 + C-1-1|1,-1>1|1,-1>2

    Now I believe I am supposed to apply the L- operator to both sides since L-|2,-2,11>=0 and since L-=L1- + L2- and we apply this to the othner side of the equatio.

    However what we get does not look very pretty.

    Am I on the right track? And what should I be doing to get the right answer?
     
    Last edited: Feb 19, 2005
  2. jcsd
  3. Feb 19, 2005 #2
    Remember |m| <= l, so we a state like l=1, m=-2 does not exist.. I think you should just have the last term in your expansion.. (someone correct me if I'm wrong, because it's been a while since I've done this.
     
  4. Feb 19, 2005 #3
    Thanks, you are totally right. I remembered l>=m but forgot that -m where m>l cannot exist. Then wouldn't it just be a 100 perent possibility that -h is the angular moment for L1 and L2?
     
  5. Feb 19, 2005 #4

    dextercioby

    User Avatar
    Science Advisor
    Homework Helper

    I didn't really undertstand much thing of your notation...It would be perfect,if were able to use the latex...
    The theorem of Clebsch & Gordan states that
    [tex] |j,m\rangle =\sum_{j_{1},j_{2},m_{1},m_{2}} \langle j_{1},m_{1},j_{2},m_{2}|j,m\rangle |j_{1},m_{1},j_{2},m_{2}\rangle [/tex]

    ,where i hope you're familiar with the notation...

    Daniel.
     
    Last edited: Feb 19, 2005
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Coupled Angular Momentum sates and probability
Loading...