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-MonteiroCentro 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
