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Journal of Physics A Mathematical and General

Calogero-Sutherland oscillator: classical behaviour and coherent states

G. S. Agarwal, S. Chaturvedi

Published Oct 21, 1995• 24 citations
Publisher

Abstract

Two kinds of coherent states are constructed in the context of the Calogero-Sutherland singular oscillator. The motion of the peaks of the wavefunctions of these coherent states are compared with the classical trajectory. It is found that while the wavefunction for one kind of coherent states is always singly peaked, that for the other acquires multiple peaks close to the classical turning point near the origin. The two coherent states are found to exhibit a kind of complementarity.

DOI
10.1088/0305-4470/28/20/009

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Two kinds of coherent states are constructed in the context of the Calogero-Sutherland singular oscillator. The motion of the peaks of the wavefunctions of these coherent states are compared with the classical trajectory. It is found that while the wavefunction for one kind of coherent states is always singly peaked, that for the other acquires multiple peaks close to the classical turning point near the origin. The two coherent states are found to exhibit a kind of complementarity.
Exact coherent states in the Calogero–Sutherland models (of time-dependent parameters) which describe identical harmonic oscillators interacting through inverse-square potentials are constructed, in terms of the classical solutions of a harmonic oscillator. For quasi-periodic coherent states of the time-periodic systems, geometric phases are evaluated. For the AN-1 Calogero–Sutherland model, the phase is calculated for a general coherent state. The phases for other models are also considered.
The main characteristics of the quantum oscillator coherent states including the two-particle Calogero interaction are investigated. We show that these Calogero coherent states are the eigenstates of the second-order differential annihilation operator which is deduced via R-deformed Heisenberg algebra or Wigner-Heisenberg algebraic technique and correspond exactly to the pure uncharged-bosonic states. They possess the important properties of non-orthogonality and completeness. The minimum uncertainty relation for the Calogero interaction coherent states is investigated. New sets of even and odd Wigner oscillator coherent states are pointed out.