Degeneracy Breaking of Hydrogen Atom

TL;DR

This paper explains how an external magnetic field causes symmetry breaking in the hydrogen atom, leading to the Zeeman effect and splitting of degenerate energy levels into new irreducible representations.

Contribution

It explicitly demonstrates the symmetry breaking process and the association of new energy levels with irreducible representations of the altered symmetry group.

Findings

Degeneracy of hydrogen atom energy levels is broken by magnetic field.

New energy levels correspond to irreducible representations of the new symmetry group.

The Zeeman effect is explained through symmetry group analysis.

Abstract

The three dimensional rotation group, SO(3), is a symmetry group of the normal hydrogen atom. Each reducible representation of this group can be associated with a degenerate energy level. If this atom is placed in an external magnetic field, the interaction between the orbital magnetic moment with this field will lead to a symmetry breaking where the symmetry group of the atom is a new group distinct from the SO(3) group. This phenomenon describes the normal Zeeman effect, where a degenerate energy level splits into several new energy levels. It is explicitly shown that each of the new energy levels can be associated with an irreducible representation of the new symmetry group.