On the harmonic oscillator properties in a twisted Moyal plane

TL;DR

This paper investigates the harmonic oscillator in a twisted Moyal plane using an operator method, revealing that its spectrum and states resemble those in ordinary Moyal space but with different parameters, contrasting previous unexpected results.

Contribution

It introduces an operator-based approach to analyze the harmonic oscillator in twisted Moyal space, providing clearer insights into its spectrum and states compared to prior Moyal-star-algebraic methods.

Findings

Spectrum and states are similar to those in ordinary Moyal space.

Differing parameters affect the physical spectrum.

Contrasts with previous results showing infinite degeneracy.

Abstract

This work prolongs, using an operator method, the investigations started in our recent paper J. Math. Phys. 51., 102108 on the spectrum and states of the harmonic oscillator on twisted Moyal plane, where rather a Moyal-star-algebraic approach was used. The physical spectrum and states of the harmonic oscillator on twisted Moyal space, obtained here by solving the corresponding differential equation, are similar to those of the ordinary Moyal space, with different parameters. This fortunately contrasts with the previous study which produced unexpected results, i.e. infinitely degenerate states with energies depending on the coordinate functions.