Symmetry and degeneracy, exceptional point and coalescence: a pedagogical approach

TL;DR

This paper presents a simple pedagogical non-Hermitian matrix model demonstrating degeneracy and coalescence at exceptional points, suitable for teaching advanced quantum mechanics concepts.

Contribution

It introduces a straightforward $3\times 3$ non-Hermitian matrix model illustrating degeneracy, coalescence, and symmetry aspects at exceptional points for educational purposes.

Findings

Model exhibits eigenvalue degeneracy and coalescence at exceptional points

Symmetry group responsible for degeneracy analyzed

Suitable for undergraduate and graduate quantum mechanics courses

Abstract

We show a parameter-dependent $3\times 3$ non-Hermitian matrix that exhibits both degeneracy and coalescence of eigenvalues at an exceptional point (Hermitian and non-Hermitian degeneracies). This simple non-Hermitian model is suitable for the discussion of those concepts in an undergraduate or graduate course on quantum-mechanics. We also study the symmetry group responsible for the degeneracy.