Non-Commutative Corrections to the MIC-Kepler Hamiltonian

TL;DR

This paper investigates how non-commutative geometry modifies the MIC-Kepler system, revealing a new linear Stark effect term absent in the traditional hydrogen atom model.

Contribution

It provides the first computation of non-commutative corrections to the MIC-Kepler Hamiltonian, highlighting the emergence of a linear Stark effect.

Findings

Identification of non-commutative corrections in Cartesian and parabolic coordinates

Discovery of a linear Stark effect term in the spectrum

Absence of simple analytic solutions for full spectrum corrections

Abstract

Non-commutative corrections to the MIC-Kepler System (i.e. hydrogen atom in the presence of a magnetic monopole) are computed in Cartesian and parabolic coordinates. Despite the fact that there is no simple analytic expression for non-commutative perturbative corrections to the MIC-Kepler spectrum, there is a term that gives rise to the linear Stark effect which didn't exist in the standard hydrogen model.