Many-body systems and identical particles

Equipment

• Two Gaussian packets superposed in the symmetric or antisymmetric combination
• “Packet separation” slider (0–5)
• “Overlap” slider (0–1)
• Occupation-number panel of the spin-orbitals

Procedure

1. Bring the two packets together

   Lower “Packet separation” to 0: in the fermion combination the two-particle density develops a node at coincident positions and vanishes — two fermions cannot share a state; in the boson combination the coincidence region is enhanced.

2. Change the overlap and explain via symmetry

   Sweep “Overlap” and compare $|\psi_S|^2$ with $|\psi_A|^2$: the two-particle amplitude is $\psi_{S/A} \propto \phi_a(x_1)\phi_b(x_2) \pm \phi_b(x_1)\phi_a(x_2)$; the interference term with the plus sign lets bosons bunch, the minus sign forces a node at $x_1 = x_2$.

3. Read the occupation panel and state the Pauli principle

   Move to the “Occupation states” panel: each spin-orbital holds at most one fermion — the label « forbidden for fermions ». Explain why two electrons may still share one spatial orbital if their spins are opposite: they occupy two different spin-orbitals.

Simulation

Experiment history

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