Analytic Solution of a Relativistic Two-dimensional Hydrogen-like Atom in a Constant Magnetic Field

TL;DR

This paper derives exact relativistic solutions for a 2D hydrogen-like atom in a magnetic field, revealing differences from non-relativistic models, notably the absence of s states in the spectrum.

Contribution

It provides the first exact analytic solutions for the relativistic 2D hydrogen atom in a magnetic field, including energy spectra for specific field strengths.

Findings

Relativistic spectrum lacks s states.

Analytic energy solutions are obtained for certain magnetic field values.

Comparison shows differences from non-relativistic cases.

Abstract

We obtain exact solutions of the Klein-Gordon and Pauli Schroedinger equations for a two-dimensional hydrogen-like atom in the presence of a constant magnetic field. Analytic solutions for the energy spectrum are obtained for particular values of the magnetic field strength. The results are compared to those obtained in the non-relativistic and spinless case. We obtain that the relativistic spectrum does not present s states.