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Help about Pauli spin matrix

  • Thread starter InGaAsP
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  • #1
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Homework Statement



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

Homework Equations





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:

Answers and Replies

  • #2
Galileo
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Homework Helper
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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
 
  • #3
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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
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:
  • #4
nrqed
Science Advisor
Homework Helper
Gold Member
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Homework Statement



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

Homework Equations





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.
Yes, there is a mistake in the question. There really should be a factor fo 2 there.
 
  • #5
Galileo
Science Advisor
Homework Helper
1,989
6
Indeed, your first lines should be [itex]\sigma_y\sigma_z-\sigma_z\sigma_y=2i\sigma_x[/itex] etc.
 

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