Solve the Gross-Pitaevskii equation and evaluate the mean field energy, see equations (11.2.21) and (11.2.23), for an isotropic harmonic oscillator trap with frequency \(\omega_{0}\) for the case \(N a / a_{\text {osc }} \gg 1\) by ignoring the kinetic energy term. Reproduce the results (11.2.25) through (11.2.28).