Calogero–Moser Integrable Particles

Lax pair integrability & inverse-square repulsion on the line
Particles N 5
Coupling g² 2.0
Confining ω 0.5
Speed
E = —
P = —
I₂ = —
The Calogero–Moser system H = Σ pi²/2 + g²Σi≠j1/(xi−xj)² + ω²Σxi²/2 is exactly integrable via the Lax pair Lij = piδij − ig(1−δij)/(xi−xj). The N eigenvalues of L are conserved quantities (Tr Lk = const) guaranteeing non-crossing.