How is it exactly i convert between a k-space sum an integral?(adsbygoogle = window.adsbygoogle || []).push({});

Assume that we have some macroscopic solid. Periodic boundary conditions leads to kx,ky,kz = 2π/L, so each k-space state fills a volume (2π/L)^{3}or has a density of V/(2π)^{3}. To then count for instance the number of state with wavevector k<k0, what do you then do?

Intuitively I would multiply the volume of a cube of radius k0, but how does this translate into an integral exactly?

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# K space sum to integral

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