Non-relativistic solutions for three-body molecules within a Chern-Simons model

TL;DR

This paper numerically investigates the ground state energies and wave functions of four different molecules in a 2D Chern-Simons potential, comparing results with previous planar and 3D Coulomb studies.

Contribution

It provides new numerical solutions for molecular bound states within a 2D Chern-Simons framework, extending prior theoretical models.

Findings

Ground state energies and wave functions obtained for four molecules.

Comparison shows differences with previous planar and 3D Coulomb models.

Numerov method effectively applied to solve the Schrödinger equation in this context.

Abstract

The wave functions and the ground state energies for the bound states of four different muonic and electronic molecules, governed by the Chern-Simons potential in two spatial dimensions, are numerically obtained with the Numerov method. The new results are compared with former planar configuration studies that consider the attractive potential as being proportional to $\ln(\rho)$, as well as with the three-dimensional analogs assuming a Coulomb potential.