IJPAM: Volume 71, No. 3 (2011)

TOPOLOGICAL SPECTRUM OF
THE HARMONIC OSCILLATOR

Francisco Nettel$^1$On sabbatical leave from Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Hernando Quevedo$^2$
$^1$Instituto de Ciencias Nucleares
Universidad Nacional Autónoma de México
AP 70543, México D.F., 04510, MÉXICO
$^2$Dipartimento di Fisica
Università di Roma
5, Piazzale Aldo Moro, I-00185, Roma, ITALY
ICRANet, P. le della Repubblica 10, I-65122 Pescara, ITALY


Abstract. We present a derivation of the canonical energy spectrum of the harmonic oscillator by using the approach of topological quantization. The topological spectrum is derived by analyzing the Euler characteristic class of a particular principal fiber bundle in which the base space corresponds to the configuration manifold, equipped with a Jacobi metric, and the standard fiber is represented by the rotation group. The resulting topological spectrum is shown to be equivalent to the energy spectrum following from the application of the standard procedure of canonical quantization.

Received: August 9, 2009

AMS Subject Classification: 46L65, 81S99

Key Words and Phrases: topological quantization, topological spectrum, canonical spectrum

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2011
Volume: 71
Issue: 3