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Paper IPM / P / 6542  


Abstract:  
We prove that the dynamical system characterized by the Hamiltonian H=λN Σ_{j}^{N} p_{j} + μ∑_{j,k}^{N} (p_{j}p_{k})^{1/2}{cos[ν(q_{j}−q_{k})]} 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 actionangle variables and solve the
initial value problem in a very simple form.
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