Two-dimensional hydrogen-like atom in a uniform magnetic field. Large-order perturbation theory

TL;DR

This paper applies the hypervirial perturbation method to calculate high-order corrections for a 2D hydrogen-like atom in a magnetic field, demonstrating an efficient analytical approach compared to Green function methods.

Contribution

It introduces a simpler, more efficient hypervirial perturbation method for large-order corrections in 2D hydrogen-like atoms under magnetic fields.

Findings

Analytical expressions for perturbation corrections derived.

Large-order corrections computed for specific quantum states.

Method outperforms Green function-based approaches.

Abstract

The well known hypervirial perturbation method (HPM)\ based on hypervirial relations and the Hellmann-Feynman theorem is suitable for the calculation of perturbation corrections of large order for the two-dimensional hydrogen-like atom in a uniform magnetic field. We show analytical results in terms of the quantum numbers and large order corrections for particular states. This approach appears to be simpler and more efficient than the recently proposed one based on Green functions.