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Angular momentum Question

  1. Mar 7, 2005 #1
    Show that the following superposition state in the |l,m1;ms> basis:-(2/3)^1/2|1,-1;1/2> + (1/3)^1/2|1,0;-1/2> is an eigenstate of J^2 and L * S and determine the corresponding eigenvalues.

    I have no clue how to start this. Any help would be appreciated.
     
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  3. Mar 7, 2005 #2

    dextercioby

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    How do you determine the action of the operators
    [tex] \hat{\vec{J}}^{2} ,\hat{\vec{L}}^{2},\hat{\vec{S}}^{2} [/tex]

    on any eigenstate...?

    Daniel.
     
  4. Mar 7, 2005 #3

    Tom Mattson

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    First note that:

    [tex]\hat{\mathbf {J}}^2=\hat{\mathbf {J}} \cdot \hat {\mathbf {J}}=(\hat{\mathbf {L}} + \hat{\mathbf {S}}) \cdot (\hat{\mathbf {L}} + \hat{\mathbf {S}}) =\hat{\mathbf {L}}^2 + \hat{\mathbf {S}}^2+2 \hat{\mathbf {L}} \cdot \hat{\mathbf {S}}[/tex]

    Hit each term of your state vector with it.

    edit: Bloody dexter, his LaTeX is faster than mine. :tongue2:
     
    Last edited: Mar 7, 2005
  5. Mar 7, 2005 #4

    dextercioby

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    I used "hats" for operators,that's a reason for envy...:wink: :tongue:

    Daniel.

    P.S.BTW,i resent the boldface notation of vectors... :yuck: :tongue2:
     
    Last edited: Mar 7, 2005
  6. Mar 7, 2005 #5

    Tom Mattson

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    Nothing a quick edit can't fix. Now my operators don't have cold heads. :rofl:
     
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