Quantum Oscillators in the Canonical Coherent States

TL;DR

This paper investigates the properties of quantum oscillator coherent states, including those with Calogero interaction, highlighting their algebraic structure, non-orthogonality, completeness, and uncertainty relations.

Contribution

It introduces Calogero coherent states as eigenstates of a second-order annihilation operator derived from R-deformed algebra, expanding the understanding of quantum oscillator states.

Findings

Calogero coherent states are eigenstates of a second-order differential annihilation operator.

These states exhibit non-orthogonality and completeness properties.

The minimum uncertainty relation for these states is analyzed.

Abstract

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.