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\sect{Harmonic oscillators, Debye model}

Find expressions for the heat capacity in Debye model. 
Make the calculation for a general spectral density $\omega^{\alpha-1}$  
with high frequency cutoff $\omega_c$. Write specific results 
for $d=1,2,3$ given that the velocity of sound is~$c$ 
and the linear size of the medium is~$L$. Write a remark 
on the contribution of non-acoustic modes of vibrations. 
