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 Dec 2 revised Scalar product between Fock states added 2 characters in body Nov 30 revised Scalar product between Fock states added 51 characters in body Nov 30 awarded Scholar Nov 30 accepted Scalar product between Fock states Nov 30 comment Scalar product between Fock states Ok, thank you very much (which is actually the answer I would got expanding the equation which is in the comment I wrote just above). I have to deal with the computation of all the possible permutations...I will let the computer do it for me...:) Nov 30 comment Scalar product between Fock states If I use your recipe I get: \begin{align} \langle \dots \tilde{n}_k\dots |n_1 \dots n_L \rangle & = \langle | \prod_k \left( \hat{b}_k \right)^{\tilde{n}_k } |n_1 \dots n_L \rangle \\ & = \langle | \prod_k \left( \frac{1}{\sqrt{L}} \sum_j e^{-ikj} \hat{a}_j \right)^{\tilde{n}_k } |n_1 \dots n_L \rangle \end{align} even if now it is quite straightforward which are the terms that survive (the ones that annihilate $|n_1 \dots n_L \rangle$ ) I'm not able to find a "clean" and useful equation ... :( Nov 30 comment Scalar product between Fock states You are right, I edited the question and changed the notation. Anyway, the question is about Fock states in different bases otherwise the answer would be trivial. And of course the two states have the same number of bosons: $\sum_k \tilde{n}_k = \sum_j n_j$. Nov 30 awarded Editor Nov 30 revised Scalar product between Fock states added 24 characters in body Nov 30 awarded Student Nov 30 asked Scalar product between Fock states