Spontaneous Symmetry Breakdown in non-relativistic Quantum Mechanics

TL;DR

This paper discusses the pedagogical use of simple non-relativistic quantum models to illustrate spontaneous symmetry breakdown, highlighting a toy model that demonstrates this phenomenon.

Contribution

It introduces a simple quantum-mechanical toy model showing spontaneous symmetry breakdown, aiding understanding of this concept in non-relativistic quantum mechanics.

Findings

Toy model exhibits spontaneous symmetry breakdown

Highlights pedagogical advantages of simple models

Discusses pros and cons of existing models

Abstract

The advantages and disadvantages of some pedagogical non-relativistic quantum-mechanical models, used to illustrate spontaneous symmetry breakdown, are discussed. A simple quantum-mechanical toy model (a spinor on the line, subject to a magnetostatic interaction) is presented, that exhibits the spontaneous breakdown of an internal symmetry.