Quantum oscillator as 1D anyon

Abstract

It is shown that in one spatial dimension the quantum oscillator is dual to the charged particle situated in the field described by the superposition of Coulomb and Calogero-Sutherland potentials.

9 pages, LaTex

References in corpus (2)

• Hidden Symmetry of the Yang--Coulomb System
• 8D oscillator as a hidden SU(2) - monopole

Cited by in corpus (6)

• The charge-dyon bound system in the spherical quantum well
• Exact and quasi-exact solvability of two-dimensional superintegrable quantum systems. I. Euclidean space
• About dual one-dimensional oscillator and Coulomb-like theories
• About dual two-dimensional oscillator and Coulomb-like theories on a plane
• Spectral geometry, homogeneous spaces, and differential forms with finite Fourier series
• About dual two-dimensional oscillator and Coulomb-like theories on pseudosphere