%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\sect{The functions $N(E)$ and $Z(T)$ for general dispersion relation}

Find the states density function ${g\left(E\right)}$ and the
distribution function ${Z\left(\beta\right)}$ for a particle that
moves in a ${d}$ dimensional space with volume ${V=L^{d}}$.

Assume the particle has dispersion relation

case a' ${E=C|P|^{\nu}}$ \\
case b' ${E=\sqrt{m^{2}+p^{2}}}$

Make sure that you know how to get a result also in the "quantal"
and the "semiclassical" way.