Eur. Phys. J. C 21, 749-756 (2001)
DOI: 10.1007/s100520100763

The quantum harmonic oscillator on a circle and a deformed Heisenberg algebra

M.A. Rego-Monteiro

Centro Brasileiro de Pesquisas Físicas, Rua Xavier Sigaud 150, 22290-180 Rio de Janeiro, RJ, Brazil

(Received: 29 March 2001 / Revised version: 17 July 2001 / Published online: 31 August 2001 -© Springer-Verlag / Società Italiana di Fisica 2001 )

Abstract
We show that the Heisenberg-type algebra describing the first levels of the quantum harmonic oscillator on a circle of large length L is a deformed Heisenberg algebra. The successive energy levels of this quantum harmonic oscillator on a circle of large length L are interpreted, similarly to the standard quantum one-dimensional harmonic oscillator on an infinite line, as being obtained by the creation of a quantum particle of frequency w at very high energies.

© Società Italiana di Fisica, Springer-Verlag 2001