Chapter 5, Problem 5.32P

(a)

To determine

The total energy $E_{tot}$ and check whether it reduces to Equation 5.56 when $N_{+}=N_{-}$.

(b)

To determine

Show that for $M/{\mu }_B\ll \rho \equiv \left(N_{+}+N_{-}\right)/V$, the energy density is $\frac{1}{V}{E}_{tot}=\frac{{\hslash }^2{\left(3{\pi }^2\rho \right)}^{5/3}}{10{\pi }^{2}m}\left[1+\frac{5}{9}{\left(\frac{M}{\rho {\mu }_B}\right)}^2\right]$.