The ground-state pressure of an interacting Bose gas (see Lee and Yang, 1960a) turns out to be

\[P_{0}=\frac{\mu_{0}^{2} m}{8 \pi a \hbar^{2}}\left[1-\frac{64}{15 \pi} \frac{\mu_{0}^{1 / 2} m^{1 / 2} a}{\hbar}+\cdots\right]\]

where \(\mu_{0}\) is the ground-state chemical potential of the gas. It follows that

\[n \equiv\left(\frac{d P_{0}}{d \mu_{0}}\right)=\frac{\mu_{0} m}{4 \pi a \hbar^{2}}\left[1-\frac{16}{3 \pi} \frac{\mu_{0}^{1 / 2} m^{1 / 2} a}{\hbar}+\cdots\right]\]

and \[\frac{E_{0}}{V} \equiv\left(n \mu_{0}-P_{0}\right)=\frac{\mu_{0}^{2} m}{8 \pi a \hbar^{2}}\left[1-\frac{32}{5 \pi} \frac{\mu_{0}^{1 / 2} m^{1 / 2} a}{\hbar}+\cdots\right]\]
Eliminating \(\mu_{0}\) from these results, derive equations (11.3.16) and (11.3.17).