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Homework Help: Help about Pauli spin matrix

  1. Mar 20, 2007 #1
    1. The problem statement, all variables and given/known data

    prove the idendity [tex] \sigma \times \sigma =i \sigma [/tex] where [tex] \sigma[/tex] is Pauli Spin matrices

    2. Relevant equations



    3. The attempt at a solution

    This is how I did..and I am getting
    2[tex] i \sigma [/tex] instead of [tex] i\sigma [/tex].

    http://i146.photobucket.com/albums/r273/soorajr/paulimatrix.jpg

    This question was asked twice for the university exam, and during both times, they asked us to prove [tex] \sigma \times \sigma =i \sigma [/tex].
    Did i make any mistake? or the examiner was wrong?
    Thanks in advance.
     
    Last edited: Mar 20, 2007
  2. jcsd
  3. Mar 20, 2007 #2

    Galileo

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    You wrote (for instance) [itex]\sigma_y\sigma_z-\sigma_z\sigma_y=i\sigma_x[/itex]
    but then later when you get the same expression for the x-component you enter
    [itex]i\sigma_x+i\sigma_x[/itex], which is where your factor 2 comes from.
    Check the middle line in your calculation of the determinant again
     
  4. Mar 20, 2007 #3
    Thanks Galileo for ur reply

    the results i used were[tex]\sigma_x\sigma_y=-\sigma_y\sigma_x=i\sigma_z[/tex]
    i changed x,y,z cyclicly, and hence reached at 2[tex]i \sigma[/tex]
    do u think I am supposed to get only i[tex] \sigma[/tex] instead of 2i[tex] \sigma[/tex]
    thanks in advance
     
    Last edited: Mar 20, 2007
  5. Mar 20, 2007 #4

    nrqed

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    Yes, there is a mistake in the question. There really should be a factor fo 2 there.
     
  6. Mar 20, 2007 #5

    Galileo

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    Indeed, your first lines should be [itex]\sigma_y\sigma_z-\sigma_z\sigma_y=2i\sigma_x[/itex] etc.
     
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