PX284 - N1 - recap

f (E) = \frac{1}{\exp (β (E - μ)) \pm 1}

where, $+$ for fermions, $-$ for bosons

\begin{matrix} N = \int_{0}^{\infty} g (E) f (E) d E \\ U = \int_{0}^{\infty} E g (E) f (E) d E \\ g (E) d E = (2 s + 1) \frac{V}{(2 π)^{2}} {(\frac{2 m}{ℏ^{2}})}^{3 / 2} E^{1 / 2} d E \end{matrix}