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Homework Help: Many Body bogoliubov transformation

  1. Dec 6, 2016 #1

    Hl3

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    1. The problem statement, all variables and given/known data
    The occupation of each single-particle state with wave vector k =/= 0 in the ground state is given by nk = <0|bkbk|0>
    where b and b† are bogoliubov transformaition. Find an expression for nk.

    bk = cosh(θ)ak - sinh(θ) a-k
    bk = cosh(θ)ak - sinh(θ)a-k
    2. Relevant equations


    3. The attempt at a solution
    I don't fully understand the notaition with zeros. I belive nk would equal to 0, however question asks for the expression for nk. thnaks in advance
     
  2. jcsd
  3. Dec 6, 2016 #2
    No, it is not. The state ##|0>## is the vacuum of the annihilation operators ##a_k##. That is,
    $$a_k|0>=0$$ for all ##k##, but
    $$b_k|0>\neq 0$$ (unless ##\theta =0##).
     
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