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Construct States from Clebsch-Gordon Coefficients

  1. Jan 31, 2016 #1
    1. The problem statement, all variables and given/known data

    Hello all,
    Im asked to construct the state [itex] | \frac{5}{2} , \frac{3}{2} \rangle [/itex] from the eigenfunctions [itex] | L, L_z\rangle [/itex] and the electron states [itex] | \uparrow \rangle [/itex] and [itex] | \downarrow \rangle [/itex].

    2. Relevant equations

    Clebsch Gordon Coefficient's table

    3. The attempt at a solution

    To be honest, im not sure how to get started. My book does not explain how to construct states from the eigenfunctions [itex] | L, L_z\rangle [/itex] and the electron states [itex] | \uparrow \rangle [/itex] and [itex] | \downarrow \rangle [/itex]. Can anyone point me in the right direction? Thanks!
     
  2. jcsd
  3. Feb 1, 2016 #2

    blue_leaf77

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    Are you asked to write an eigenstate of the total angular momentum ##\mathbf{J} = \mathbf{L} + \mathbf{S}## (which is in this case ##|5/2,3/2\rangle##) in terms of the individual eigenstates of ##\mathbf{L}## and ##\mathbf{S}##? If yes, the easiest way is just to look up in the table of Clebsch-Gordan coefficients which you can find online.
     
    Last edited: Feb 1, 2016
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