# Anisotropic Features of the Two-dimensional Hydrogen Atom in a Magnetic Field

## TL;DR

This study numerically investigates how a magnetic field induces anisotropic effects on the ground state energy and wave function of a two-dimensional hydrogen atom, revealing a strong angular dependence and energy reduction.

## Contribution

It provides the first detailed numerical analysis of the anisotropic characteristics of a 2D hydrogen atom in a magnetic field, considering finite proton mass.

## Key findings

- GSE depends non-linearly on the angle between magnetic field and electron plane normal.
- GSE can decrease up to 1.9 times as the angle approaches 90 degrees.
- Significant anisotropic effects are observed across various magnetic field strengths.

## Abstract

The aim of the current work is the numerical research of the anisotropic characteristics of the two-dimensional hydrogen atom induced by a magnetic field. The ground state energy (GSE) of the two-dimensional hydrogen atom and the corresponding wave function have been numerically calculated in the Born-Oppenheimer approximation and with taking into account the finite mass of the proton. The non-linear dependence of GSE on the angle {\alpha} between the magnetic field vector and the normal to the plane of electron motion in a wide range of magnetic field strength has been found. The effect of a significant reduction of GSE (up to 1.9-fold) is observed with increasing the angle {\alpha} up to 90 degrees.