# Normalization of debye

Hi Members,
We know that in Debye model, the phonon spectrum is given by g($$\omega$$)=Const.$$\omega^2$$. And if we have N atoms and so 3N normal modes..so 3N=integral of g($$\omega$$)d$$\omega$$ and solving by simple integration rule we get Const. = 9N/($$\omega^3_D$$).
Now my problem is how to get it Normalized equation..g($$\omega$$)=???(1).
In books i see g($$\omega$$)=3$$\omega^2$$/$$\omega^3_D$$.
I just need to know how to derive g($$\omega$$)=3$$\omega^2$$/$$\omega^3_D$$???
Please explain me clearly every step for such derivation..And in general how to normalizes a function step by step ???