A solvable Hamiltonian system: Integrability and action-angle variables

Journal Article · Sat Mar 01 04:00:00 EST 1997 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.531907· OSTI ID:467259

Karimipour, V ^[1]

---

1. Institute for Studies in Theoretical Physics and Mathematics, P.O. Box 19395-5531, Tehran (Iran)

We prove that the dynamical system characterized by the Hamiltonian H={lambda}N{summation}{sub j}{sup N}p{sub j}+{mu}{summation} {sub j,k}{sup N}(p{sub j}p{sub k}){sup 1/2}{l_brace}cos[{nu}(q{sub j}{minus}q{sub k})]{r_brace} proposed and studied by Calogero [J. Math. Phys. {bold 36}, 9 (1994)] and Calogero and van Diejen [Phys. Lett. A {bold 205}, 143 (1995)] is equivalent to a system of {ital 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.{copyright} {ital 1997 American Institute of Physics.}

• OSTI ID: 467259
• Journal Information: Journal of Mathematical Physics, Journal Name: Journal of Mathematical Physics Journal Issue: 3 Vol. 38; ISSN JMAPAQ; ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
ACTION INTEGRAL
CLASSICAL MECHANICS
DYNAMICS
HAMILTONIANS
HARMONIC OSCILLATORS
QUANTUM MECHANICS