On noncommutative isotropic harmonic oscillator

TL;DR

This paper investigates how noncommutativity affects the energy spectrum of the isotropic harmonic oscillator, revealing degeneracy patterns linked to an sU(2) algebra for many values of the noncommutativity parameter.

Contribution

It explicitly constructs the algebra responsible for degeneracy in the noncommutative isotropic harmonic oscillator's spectrum.

Findings

Spectrum degeneracy occurs at dense set of theta values.

The algebra responsible for degeneracy is always sU(2).

Generators of the algebra are explicitly constructed.

Abstract

Energy spectrum of isotropic oscillator as a function of noncommutativity parameter theta is studied. It is shown that for a dense set of values of theta the spectrum is degenerated and the algebra responsible for degeneracy can be always chosen to be sU(2). The generators of the algebra are constructed explicitely.