Solving two-dimensional non-relativistic electronic and muonic atoms governed by Chern-Simon potential

TL;DR

This paper numerically solves two-dimensional electronic and muonic atoms with Chern-Simons potential, comparing their eigenvalues and eigenfunctions to those with traditional potentials in 2D and 3D.

Contribution

It introduces a modified Numerov method to solve for eigenvalues and eigenfunctions of 2D atoms governed by Chern-Simons potential, a novel approach in this context.

Findings

Eigenvalues and eigenfunctions are computed for 2D atoms with Chern-Simons potential.

Comparison shows differences between Chern-Simons and $1/r$ potentials in 2D and 3D.

Results highlight the impact of the Chern-Simons potential on atomic properties.

Abstract

Bidimensional muonic and electronic atoms, with nuclei composed of a proton, deuteron, and triton, and governed by Chern-Simons potential, are numerically solved. Their eigenvalues and eigenfunctions are determined with a slightly modified Numerov method. Results are compared with those assuming that the same atoms are governed by the usual $1/r$ potential even in a two-dimensional space, as well as with its three-dimensional analogs.