# "A Solvable Hamiltonian System" Integrability and Action-Angle Variables

Physics – High Energy Physics – High Energy Physics - Theory

Scientific paper

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## Details "A Solvable Hamiltonian System" Integrability and Action-Angle Variables "A Solvable Hamiltonian System" Integrability and Action-Angle Variables

12 pages, Latex, No Figures

Scientific paper

10.1063/1.531907

We prove that the dynamical system charaterized by the Hamiltonian $H = \lambda N \sum_{j}^{N} p_j + \mu \sum_{j,k}^{N} {{(p_j p_k)}^{1\over 2}} \{ cos [ \nu ( q_j - q_k)] \}$ proposed and studied by Calogero [1,2] is equivalent to a system of {\it non-interacting} harmonic oscillators. We find the explicit form of the conserved currents which are in involution. We also find the action-angle variables and solve the initial value problem in simple form.

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