Hi all,(adsbygoogle = window.adsbygoogle || []).push({});

In Charles Kittel (Introduction to Solid State Physics) He writes :

U (Total Phonon Energy ) = Σ_{k}∑_{p}((ħ*ω_{k,p})/((exp(ħ*ω_{k,p}/τ))-1))

I understand this, but then he integrate over k and multiply by density of states :

U (Total Phonon Energy ) = ∑_{p}∫dω*D_{p}(ω)*((ħ*ω_{k,p})/((exp(ħ*ω_{k,p}/τ))-1))

I understand the Integration, but why multiply by density of states, if he wants to change the variable dk to dω why not just use the dispersion relation i.e k=g(ω) so dk=(the first dervative g(ω))*dω , dk=dω/V_{g}

so it be :

U (Total Phonon Energy ) = ∑_{p}∫dω*(1/V_{g})*((ħ*ω_{k,p})/((exp(ħ*ω_{k,p}/τ))-1))

Thanks in Advance.

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# Phonon Energy and Density of States

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