Analytic computation of the energy levels of a two-dimensional hydrogenic donor in a constant magnetic field

TL;DR

This paper presents an analytic approach to calculating the energy levels of a two-dimensional hydrogenic donor in a magnetic field, using a mixed-basis variational method and comparing it with other numerical techniques.

Contribution

It introduces a variational method for computing 2D hydrogenic energy levels in magnetic fields and validates it against other numerical methods.

Findings

Variational solutions are accurate in weak and strong magnetic fields.

Energy spectra computed match well with other numerical methods.

The method effectively captures the behavior across different regimes.

Abstract

We compute the energy levels of a 2D Hydrogen atom when a constant magnetic field is applied. With the help of a mixed-basis variational method, we calculate the energy eigenvalues of the 1S, 2P- and 3D- levels. We compare the computed energy spectra with those obtained via a generalization of the mesh point technique as well as the shifted 1/N method. We show that the variational solutions present a good behavior in the weak and strong magnetic field regimes.