Use the dimensionless form from problem 11.17. Ignoring the kinetic energy term

\[
\psi=\frac{\sqrt{\tilde{\mu}-\frac{s^{2}}{2}}}{\sqrt{4 \pi N a / a_{0}}} .
\]

The normalization is

\[
1=\frac{4 \pi a_{0}}{4 \pi N a} \int_{0}^{\sqrt{2 \tilde{\mu}}}\left(\tilde{\mu}-\frac{s^{2}}{2}ight) d s
\]

which gives

\[
N=\frac{a_{0}}{15 \pi a}(2 \tilde{\mu})^{5 / 2}
\]

Using the definitions for \(u_{0}, \tilde{\mu}\), and \(a_{0}\) gives equations (11.2.25) and (11.2.26). Equation (11.2.28) follows from the definition of the dimensionless length scale, and (11.2.27) comes from integrating the dimensionless energy in problem 11.17, again ignoring the kinetic energy term.