[QUE/SM-03004] SM-PROBLEM

Consider an isolated system of ideal gas of $N$ molecules
contained in a volume $V$ and having an energy
$$E=\sum_{i=1}^{3N}\frac{p_i^2}{2m}.$$ Show that the number of states in the
energy range $U-\Delta$ and $U$ is
of the system is given by\hfill [5]
\begin{eqnarray*}
\frac{1}{\Gamma(3N/2+1)}\frac{3N\Delta}{2U} \Big(\frac{mU V^{2/3}
}{2\pi\hbar^2}\Big)^{3N/2}
\end{eqnarray*}