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I need to determine the adjoint operator to $a_i$:

$a_i |n_0, n_1, ... \rangle_S = \sqrt{n_i} |n_0, n_1, ..., n_{i-1}, n_i - 1, n_{i+1}, .. \rangle_S$

where the $S$ should denote the symmetrizer. I just don't know how to determine the adjoint, we have done this only for "simple" operators.

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  • $\begingroup$ I think symmetrizer is not needed in the Fock states. $\endgroup$ – velut luna Jan 11 '16 at 8:44
  • $\begingroup$ With annihilation and creation operators finding the adjoint (even formally) can be a little bit tricky...but you have really just to apply carefully the definition. $\endgroup$ – yuggib Jan 11 '16 at 9:03
  • $\begingroup$ So you mean taking the $a^T$? $\endgroup$ – Darius Jan 11 '16 at 9:37