# Many Body bogoliubov transformation

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1. Dec 6, 2016

### Hl3

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. Dec 6, 2016

### eys_physics

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 $\theta =0$).