[tex]I(\vec{n}-\vec{m})=\frac{1}{N}\sum_{\vec{k}}I(\vec{k})e^{i\vec{k}(\vec{n}-\vec{m})}[/tex](adsbygoogle = window.adsbygoogle || []).push({});

[tex]I(\vec{n}-\vec{m})=\frac{1}{\sqrt{N}}\sum_{\vec{k}}I(\vec{k})e^{i\vec{k}(\vec{n}-\vec{m})}[/tex]

In which cases is better to use first and in which second relation? [tex]N[/tex] is number of knottes of lattice.

And when I can say [tex]I(\vec{n}-\vec{m})=I(|\vec{n}-\vec{m}|)[/tex]?

And is it a way to show

[tex]\sum_{\vec{k}}I(\vec{k})=\sum_{-\vec{k}}I(\vec{k})[/tex]?

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# Exchange interaction in solid state physics

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