Scaled variational computation of the energy spectrum of a two-dimensional hydrogenic donor in a magnetic field of arbitrary strength

TL;DR

This paper introduces a scaled variational method to accurately compute the energy spectrum of a two-dimensional hydrogenic donor in magnetic fields of arbitrary strength, improving understanding of quantum behavior under magnetic influence.

Contribution

The paper presents a novel scaled variational approach combined with a generalized virial theorem for calculating energy levels of a 2D hydrogen atom in magnetic fields, extending previous methods.

Findings

Good agreement with mesh point and shifted 1/N methods

Accurate energy levels in weak and strong magnetic fields

Effective for multiple energy states (1S, 2P-, 3D-)

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 and a genera lization of virial theorem, which consists in scaling the wave function, we calculate the binding energies 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 very good behavior in the weak and strong magnetic field regimes.