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seen Dec 17 '12 at 9:16

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revised Scalar product between Fock states
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revised Scalar product between Fock states
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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: $\sum_k \tilde{n}_k = \sum_j n_j$.
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30
awarded  Editor
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30
revised Scalar product between Fock states
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30
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30
asked Scalar product between Fock states