Two-dimensional hydrogen-like atom in a weak magnetic field

TL;DR

This paper derives explicit analytical formulas for energy level corrections of a 2D hydrogen-like atom in a weak magnetic field, improving upon previous results and providing higher-order perturbation corrections.

Contribution

It introduces a new analytical approach using Sturmian expansion to compute higher-order energy corrections in a 2D hydrogen atom under magnetic perturbation.

Findings

Explicit formulas for energy corrections up to fourth order.

Correction of previous fourth-order energy expression for the ground state.

Enhanced understanding of magnetic effects on 2D hydrogenic systems.

Abstract

We consider a non-relativistic two-dimensional (2D) hydrogen-like atom in a weak, static, uniform magnetic field perpendicular to the atomic plane. Within the framework of the Rayleigh-Schr\"odinger perturbation theory, using the Sturmian expansion of the generalized radial Coulomb Green function, we derive explicit analytical expressions for corrections to an arbitrary planar hydrogenic bound-state energy level, up to the fourth order in the strength of the perturbing magnetic field. In the case of the ground state, we correct an expression for the fourth-order correction to energy available in the literature.