solid state physics: phonon density of state

Pistike

1. The problem statement, all variables and given/known data

There is a Ar cube crystal with Lenard jones potential: V[itex]^{L.J.}[/itex]=-[itex]\alpha[/itex]/r[itex]^{6}[/itex]+[itex]\beta[/itex]/r[itex]^{12}[/itex]

We know the volume V, the parameters of the L.J. potential, and the mass of the Ar atom (m[itex]_{Ar}[/itex]).
Determine the phonon density of state. (D(ω)=?)

2. Relevant equations
D(ω)=Ʃδ(ω-ω[itex]_{i}[/itex])

3. The attempt at a solution

I have no idea what to do with the given lenard jones potential, and its parameters. How should I calculate the dispersion relation?
1. The problem statement, all variables and given/known data



2. Relevant equations



3. The attempt at a solution