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Theory, lab and space experiments, and calculations related the physics of plasmas, i.e., matter constituted by ionized atoms.

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Plasmons : doubts about the derivation of the Heisenberg equation of electrons' density

I'm studying plasmons from "Haken-Quantum Field Theory of Solids", and i need some help in the calculation of the equation of motion of eletrons' density \begin{equation} \hat{\rho}_{\overrightarrow{q …
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Plasmons : doubts about the derivation of the Heisenberg equation of electrons' density

As regard the first doubt, From the delta Kronecker we have $$ \vec{k}_1-\vec{k}_4 = \vec{k}_3-\vec{k}_2 $$ so \begin{align*} \vec{q}'&=\vec{k}_1-\vec{k}_4 \\ &=\frac{1}{2}\left(\vec{k}_1 - \vec{k} …
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