Determine the critical number of particles for condensation at a fixed temperature in a three-dimensional harmonic potential with energy U = 1/2kr². The quantum states in a harmonic potential are discrete, with energy where ω = √k/m and degeneracy g = (n + 1)(n + 2)/2, where n = 0, 1, 2, . . .. Assume k_BT ≫ h̄ω, so that one can treat the levels as a continuum of states with energy E = nh̄ω and g = (E/h̄ω)²/2.