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Homework Help: Bloch vector from taylor expansion

  1. Nov 17, 2007 #1
    1. The problem statement, all variables and given/known data

    I need to find the bloch vector for the density matrix [itex]\frac{1}{N}\exp{-\frac{H}{-k_bT}}[/itex] where the Hamiltonian is given by [itex]H=\hbar\omega\sigma_z[/itex].

    3. The attempt at a solution

    I can break the Taylor series of exp into odd and even terms because sigma z squared is the identity. I get something that looks like sine and cosine but I'm missing i for Euler's equation. How else can I group the terms?
  2. jcsd
  3. Nov 17, 2007 #2


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    I am not going to be very helpful because I know little about Bloch vectors but why do you need to get an i factor? I don't see anything else to do here than to simply expand and get the sine and cos terms.
  4. Nov 17, 2007 #3
    Mmm I think you're right and now I feel stupid :P

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