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I have obtained the phonon dispersion curve by applied a numerical simulation. However, how can I obtain the phonon density of state from such a curve?

generally speaking,

g(q)dq = g(w)dw, here q is the wave-vector; w is the phonon frequency. g(q), g(w) is the density of quantities mentioned above. g(w) is the right one I expect to calculate. and the phonon dispersion curve provide the relation of dw/dq. from the wikipedia, I know

g(q) = V*k^2/(2*pi^3) in 3-D homogenous solid.

My question is How to transfer g(q) into a functional form of "w", in order to subsitute the "dw/dq" into it, and obtain the "g(w)" ?

Thanks

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# From phonon dispersion to density of state

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