Expectation value of X and Y component of angular momentum

  1. 1. The problem statement, all variables and given/known data
    Show:
    <Jx>=<Jy>=0

    2. Relevant equations

    Jx=1/2(J++J-)
    Jy=1/2(J+-J-)

    3. The attempt at a solution

    <jm l Jx l jm> = < jm l 1/2 J+ l jm> + < jm l j- l jm >
    = < jm l h/2 sqrt [(j-m)(j+m+1)] + h/2sqrt[(j+m)(j+m+1) l jm >

    i am not sure how to apply the next step
     
  2. jcsd
  3. Matterwave

    Matterwave 3,853
    Science Advisor
    Gold Member

    Note that |j,m> is NOT an eigenstate of either J+ or J-. In fact, J+|j,m>=k|j,m+1>, etc.

    Additionally note that [tex]<j,m|j,n>=\delta_{m,n}[/tex]
     
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