Noncommutative oscillator, symmetry and Landau problem

TL;DR

This paper explores the properties of a noncommutative isotropic oscillator, analyzing its symmetries and connections to the Landau problem, revealing how noncommutativity influences quantum behavior and symmetries.

Contribution

It introduces a detailed analysis of the noncommutative isotropic oscillator's symmetry properties and establishes a relation between noncommutative parameters and the magnetic field in the Landau problem.

Findings

Symmetry properties depend on specific relations between noncommutative parameters.

A relation between noncommutative parameters and magnetic field is derived.

Comparison between Landau problem and noncommutative oscillator highlights their connection.

Abstract

Isotropic oscillator on a plane is discussed where both the coordinate and momentum space are considered to be noncommutative. We also discuss the symmetry properties of the oscillator for three separate cases when both the noncommutative parameters \Theta and \bar{\Theta} satisfy specific relations. We compare the Landau problem with the isotropic oscillator on noncommutative space and obtain a relation between the two noncommutative parameters with the magnetic field of the Landau problem.