We evolve a complex quantum field ψ(x,y,t) with a Schrödinger-Poisson flow:
i ψ_t = -(1/2)Δψ (V_conf(x,y) G Φ(x,y,t)) ψ, with ρ=|ψ|² and ΔΦ = ρ - ⟨ρ⟩.
That bracket (V_conf GΦ) is just the potential energy landscape. V_conf is the trap you choose by hand (a smooth bowl that keeps the wave from drifting away). Φ is the field generated by the wave’s own density...compute ρ, solve the Poisson equation, feed Φ back into the evolution. G is the knob that sets how strongly the wave feels its own Φ.
Visually
Hue is phase φ=arg(ψ), brightness is density ρ^γ, the banded helicoids are phase ribbons cos(mφ θ(t)), the bright ridges are boosted by |∇ρ|, and the tiny white pearls mark vortices where the phase winding satisfies ∮∇φ·dl = 2πk.
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#QuantumMechanics #SchrodingerPoisson #ComputationalPhysics #PhysicsVisualization