On page 9 of *Quantum theory of many-particle systems* by Alexander L. Fetter and John Dirk Walecka, during the derivation of the second-quantised kinetic term, there is an equality equation below:(adsbygoogle = window.adsbygoogle || []).push({});

>\begin{align}

\sum_{k=1}^{N} \sum_{W} & \langle E_k|T|W\rangle C(E_1, ..., E_{k-1}, W, E_{k+1},...,E_N, t)

\\&=

\sum_{k=1}^{N}\sum_{W}\langle E_k|T|W\rangle\times \bar{C}(n_1, n_2,...,n_{E_k}-1, ..., n_{W}+1,...,n_\infty, t)

\end{align}

Why is the number of particles with quantum numbers n_{Ek}decreased by 1 whereas the number of particles with quantum numbers n_{W}increased by 1?

Anybody know how to get this equality?

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# A Fetter & Walecka's derivation of second-quantised kinetic term...

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