Laughlin Wavefunction

Parameters

Filling ν = 1/m, m = 3 Electrons N = 4 Magnetic length ℓ = 1.00

Drag electron pos(0,0)

|Ψ|² at probe—

Vanishing order at nodesm=3

Laughlin wavefunction (1983):

Ψ_m(z₁…z_N) = ∏_i<j(z_i−z_j)^m · exp(−Σ|z_k|²/4ℓ²)

where z = x+iy. The wavefunction vanishes as (z_i−z_j)^m when electrons meet — the Jastrow factor creates a correlation hole of order m.

m odd → fermionic antisymmetry. Filling ν=1/m. Drag the yellow probe to see how the density responds.

The density vanishes exactly when the probe coincides with any fixed electron (nodes visible as dark spots).