Thomas–Fermi approximation for trapped BEC: kinetic term dropped, μ = V(r) + g·n(r)

Thomas–Fermi approximation for a weakly-interacting trapped Bose–Einstein condensate. Setup: a macroscopic condensate wavefunction Ψ(r) with |Ψ|² = n(r); harmonic trap V_trap(r) = m·ω²·r²/2; contact interaction g·n. Governing equation:…