Zeeman Effect in Phase Space

TL;DR

This paper investigates the Zeeman effect in a 2D hydrogen atom within phase space, calculating the Wigner function using Bohlin mapping and perturbation theory, and analyzing the negativity parameter.

Contribution

It introduces a phase space approach to the Zeeman effect, employing Bohlin mapping and perturbation theory to simplify calculations of the Wigner function.

Findings

Wigner function for the Zeeman effect is computed.

Negativity parameter for the system is analyzed.

Phase space method provides new insights into magnetic effects.

Abstract

The two-dimensional hydrogen atom in an external magnetic field is considered in the context of phase space. Using solution of the Schr\"{o}dinger equation in phase space the Wigner function related to the Zeeman effect is calculated. For this purpose, the Bohlin mapping is used to transform the Coulomb potential into a harmonic oscillator problem. Then it is possible to solve the Schr\"{o}dinger equation easier by using the perturbation theory. The negativity parameter for this system is realised.