Spectrum of the harmonic oscillator in a general noncommutative phase space

TL;DR

This paper investigates the energy spectrum of a 2D harmonic oscillator in a noncommutative phase space with non-zero momentum-momentum commutators using algebraic methods, providing insights into its quantum properties.

Contribution

It introduces an algebraic approach to solve the eigenvalue problem of the harmonic oscillator in a generalized noncommutative phase space with non-vanishing momentum-momentum commutators.

Findings

Eigenvalues of the oscillator are explicitly calculated.

The noncommutative structure modifies the energy spectrum.

Results extend understanding of quantum systems in noncommutative geometries.

Abstract

Harmonic oscillator, in 2-dimensional noncommutative phase space with non-vanishing momentum-momentum commutators, is studied using an algebraic approach. The corresponding eigenvalue problem is solved and discussed.