# Show that the quantum-mechanical partition function of a system of (N) interacting particles approaches the classical form

## Question:

Show that the quantum-mechanical partition function of a system of \(N\) interacting particles approaches the classical form

\[Q_{N}(V, T)=\frac{1}{N ! h^{3 N}} \int e^{-\beta E(\boldsymbol{q}, \boldsymbol{p})} d^{3 N} q d^{3 N} p\]

as the mean thermal wavelength \(\lambda\) becomes much smaller than (i) the mean interparticle distance \((V / N)^{1 / 3}\) and (ii) a characteristic length \(r_{0}\) of the interparticle potential.

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