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Homework Help: Matrix Elements

  1. Mar 6, 2010 #1
    1. The problem statement, all variables and given/known data

    Does anyone know what the formula is for the following:

    <j m | S^2_+ |j m > = ?

    Reference to equations in Sakurai would be helpful in deriving the relation. I would suspect 3.5.37 but what about the delta_j j' ?

    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Mar 6, 2010 #2
    3.5.35 a

    <j',m|J^2 |j,m> = j(j+1)hbar^2 delta_j j' delta m m'

    3.5.37 is

    J_+ |j,m> = c_jm^+ |j,m+1>
     
  4. Mar 6, 2010 #3

    gabbagabbahey

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    Well, I'd start by calculating [itex]S_{-}|j,m\rangle[/itex]...what do you get for that?
     
  5. Mar 6, 2010 #4
    J_- |j,m> = c_{j,m}^+ |j,m-1>

    The formula that i'm interested in is :
    <j m | S^2_+ |j m > = delta_m',m+2 c_jm^+ c_j m+1 ^+

    But I don't understand how that is constructed, it's not in sakurai.
     
  6. Mar 6, 2010 #5

    gabbagabbahey

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    Well, [itex]\langle j,m|S^2_{-}|j,m\rangle=\langle j,m|(S^2_{-}|j,m\rangle)[/itex] and [itex]S^2_{-}|j,m\rangle=S_{-}(S_{-}|j,m\rangle)=[/itex]___?
     
  7. Mar 6, 2010 #6
    ok thx
     
  8. Mar 10, 2010 #7
    Normally J_+*J_- is substituted as J^2 - J_z^2+hbarJ_z

    As you described above, J_+(J_-J_+), wouldn't the content in parenthesese just cancel out?
     
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