Energy corrections due to the Non-commutative Phase-Space of the Charged Harmonic Oscillator in a constant magnetic field in 3D

Muhittin Cenk Eser, Mustafa Riza

Published 2020-08-10Version 1

In this paper, we study the effects of non-commutative quantum mechanics in three dimensions on the energy levels of a charged harmonic oscillator in the presence of a constant magnetic field in the z-direction. The extension of this problem to three dimensions proves to be non-trivial. We obtain the first-order corrections to the energy-levels in closed form in the low energy limit of weak non-commutativity.