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!

Homework Help: Commutators of Pauli Matrices

  1. Aug 5, 2013 #1
    1. The problem statement, all variables and given/known data

    Express the product

    where σy and σz are the other two Pauli matrices defined above.


    2. Relevant equations

    3. The attempt at a solution

    I'm not sure if this is a trick question, because right away both exponentials combine to give 1, where the result is simply σx

  2. jcsd
  3. Aug 5, 2013 #2
    That's the whole point of the exercise, to see that the exponentials do not combine to give 1. To do such a thing, you would have to pass [itex]exp(i\alpha\sigma^z)[/itex] to the other side of [itex]\sigma^x[/itex]. But [itex]\left[\sigma^z,\sigma^x\right]\neq0[/itex] so that you can't simply commute them.

    Hint: express the exponential as a series.
  4. Aug 7, 2013 #3
    Ah, I see what you mean, as the sum is a matrix and not a number. Silly me.
    Last edited: Aug 7, 2013
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted