Energy spectrum of the ground state of a two dimensional relativistic hydrogen atom in the presence of a constant magnetic field

TL;DR

This paper calculates the energy levels of a relativistic electron in a 2D hydrogen atom under a magnetic field, using a variational method and comparing with numerical and non-relativistic results.

Contribution

It introduces a mixed-basis variational approach to analyze the relativistic energy spectrum in a magnetic field, extending previous non-relativistic studies.

Findings

Energy levels depend on magnetic field strength

Wave functions are characterized for different field intensities

Results align with numerical and non-relativistic limits

Abstract

We compute the energy spectrum of the ground state of a 2D Dirac electron in the presence of a Coulomb potential and a constant magnetic field perpendicular to the plane where the the electron is confined. With the help of a mixed-basis variational method we compute the wave function and the energy level and show how it depends on the magnetic field strength. We compare the results with those obtained numerically as well as in the non relativistic limit.