A solvable Hamiltonian system: Integrability and action-angle variables

We prove that the dynamical system characterized by the Hamiltonian H=λN∑jNpj+μ∑ j,kN(pjpk)1/2{cos[ν(qj−qk)]} proposed and studied by Calogero [J. Math. Phys. 36, 9 (1994)] and Calogero and van Diejen [Phys. Lett. A 205, 143 (1995)] is equivalent to a system of noninteracting harmonic oscillators both classically and quantum mechanically. We find the explicit form of the conserved currents that are in involution. We also find the action-angle variables and solve the initial value problem in a very simple form.