Gross-Pitaevskii equation simulation: iℏ∂ψ/∂t = [−ℏ²∇²/2m + V(r) + g|ψ|²]ψ. A macroscopic quantum state where bosons occupy the same ground state, exhibiting superfluidity, vortex formation, and soliton propagation.
g = 500
ω = 8.0
T = 5
GPE splits density |ψ|² and phase S(r,t) — Thomas-Fermi radius: R_TF = √(2μ/mω²)
Healing length: ξ = ℏ/√(2mgn) | Speed of sound: c = √(gn/m)