The electron-lattice interaction potential is given by(adsbygoogle = window.adsbygoogle || []).push({});

[tex] V(r)=\sum_{i} Q_{i}\nabla V_{ei} \left( r- R_i\right)[/tex]

where i is a summation over lattice sites, [tex]Q_i [/tex] is the lattice site displacement, and [tex]V_{ei}[/tex] is the coulombic interaction

Now According to Mahan's book Many particle physics, 2nd ed. pg 34 ,[tex]V_{ei}(r)[/tex] has a Fourier transform of the form

[tex]V_{ei}(r)=1/N \sum_{q}V_{ei}(q) e^{jqr}[/tex]

I've had a hard time digesting this since this is a fourier summation of a periodic signal, and [tex]V_{ei}(r)[/tex] is not periodic, only a summation over all lattice sites is. Can anyone help me in pointing out what's wrong with my understanding

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# Electron Phonon Interaction Potential

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