1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Commutator, where have I gone wrong?

  1. Feb 24, 2010 #1
    This is for the Pauli Matrics 0 and 1 are different Hilbert Spaces
    [tex]\left[(I-Z)_{0}\otimes(I-Z)_{1} , Y_{0}\otimes Z_{1}\right][/tex]
    [tex]=\left((I-Z)_{0}\otimes(I-Z)_{1}\right)\left(Y_{0}\otimes Z_{1}\right)-\left(Y_{0}\otimes Z_{1}\right)\left((I-Z)_{0}\otimes(I-Z)_{1}\right) [/tex]
    [tex]=\left((I-Z)_{0}Y_{0}\otimes(I-Z)_{1} Z_{1} - Y_{0}(I-Z)_{0} \otimes Z_{1}(I-Z)_{1} [/tex]
    [tex]= (Y_{0} -Z_{0}Y_{0}) \otimes (Z-I)_{1} - ((Y_{0} + Y_{0}Z_{0})\otimes (Z-I)_{1} [/tex]
    [tex]= (Y_{0} -Z_{0}Y_{0}) \otimes (Z-I)_{1} - ((Y_{0} - Z_{0}Y_{0})\otimes (Z-I)_{1}

    I think this is wrong because I have done it long hand (i.e multiplying the matrices) and also I really, really don't want zero for an answer :).

  2. jcsd
  3. Feb 24, 2010 #2
    Fourth line, second term, I think the plus should be turned to minus..
  4. Feb 24, 2010 #3
    Thanks for your reply, sorry I still can't see it though, could you explain why?
    Thanks again.
  5. Feb 24, 2010 #4


    User Avatar
    Homework Helper
    Gold Member

    You really don't see why


  6. Feb 25, 2010 #5
    :blushing: Oops, thanks!
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook