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

Abstract

We prove that the dynamical system charaterized by the Hamiltonian $H=\lambda N{\sum }_j^N{p}_j+\mu {\sum }_{j,k}^N{(p_j{p}_k)}^{\frac{1}{2}}\{cos[\nu (q_j-q_k)]\}$ 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.

12 pages, Latex, No Figures

References in corpus (3)

• An integrable shallow water equation with peaked solitons
• Relation of The New Calogero Models and xxz Spin Chains
• Algebraic and Geometric Structure of the Integrable Models recently Proposed by Calogero

Cited by in corpus (3)

• A systematic construction of completely integrable Hamiltonians from coalgebras
• A study of open strings ending on giant gravitons, spin chains and integrability
• Analytically solvable Hamiltonians for quantum systems with a nearest neighbour interaction