Exchange Symmetry & Pauli Exclusion Node

Two identical particles in a 1D infinite square well — bosonic bunching vs. fermionic exclusion

Probability Density |ψ(x₁, x₂)|²
Fermion ψ₋: Pauli exclusion node along x₁ = x₂ diagonal
Spatial correlation ⟨(x₁ − x₂)²⟩ / L²
Fermions (ψ₋)
Bosons (ψ₊)
Independent (no symmetrization)
Energy Level Diagram
0.20
Physics Checks
P1: Fermion ψ₋(x,x) = 0 for all x — checking…
P2: |ψ₊(L/2,L/2)|² > |ψ₊(L/4,3L/4)|² — checking…
P3: K>0 → E₊ < E₋ — checking…