[QUE/SM-03010] 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 \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*}