Explicit solutions of the classical Calogero & Sutherland systems for any root system

Abstract

Explicit solutions of the classical Calogero (rational with/without harmonic confining potential) and Sutherland (trigonometric potential) systems is obtained by diagonalisation of certain matrices of simple time evolution. The method works for Calogero & Sutherland systems based on any root system. It generalises the well-known results by Olshanetsky and Perelomov for the A type root systems. Explicit solutions of the (rational and trigonometric) higher Hamiltonian flows of the integrable hierarchy can be readily obtained in a similar way for those based on the classical root systems.

18 pages, LaTeX, no figure

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Cited by in corpus (10)

• Hidden symmetries of integrable conformal mechanical systems
• Cuboctahedric Higgs oscillator from the Calogero model
• Prepotential approach to exact and quasi-exact solvabilities
• Simple unified derivation and solution of Coulomb, Eckart and Rosen-Morse potentials in prepotential approach
• Hamiltonian formulation of systems with balanced loss-gain and exactly solvable models
• Integrable coupled Li$\acute{e}$nard-type systems with balanced loss and gain
• Integrable scattering theory with higher derivative Hamiltonians
• Shape invariance in prepotential approach to exactly solvable models
• Exact Heisenberg operator solutions for multi-particle quantum mechanics
• On the Calogero-Moser solution by root-type Lax pair