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Homework Statement:

Consider general waveexcitations with a dispersion relations \omega(\vec(k)) =c \vec(k) ^(\gamma) canpropagateinddimensions(d=1,2,3)with wavevector \vec(k).
a) Determine the density of states g(\omega) for each of the dimensions d =1,2,3and arbitrary γ>0.
b) What is the corresponding powerlaw at low temperatures for the energy
E \propto T^(\alpha) and the specific heat? (Hint: The independent modes of the wave excitations can be described by the singleparticle partition function for a harmonic oscillator).
Can you please help me? :)
Relevant Equations:
 I think you have to use the delta distribution to solve part a).
I know that this is the general case of the Einstein and Debye Model.