PT-symmetric quantum mechanics

TL;DR

PT-symmetric quantum mechanics explores non-Hermitian Hamiltonians that still produce physically acceptable quantum systems, expanding the traditional framework and offering new theoretical and experimental insights.

Contribution

This review introduces PT symmetry concepts using oscillator models, providing an accessible foundation for understanding and researching non-Hermitian quantum systems.

Findings

PT-symmetric Hamiltonians can have real spectra without Hermiticity.

Oscillator models illustrate key properties of PT-symmetric quantum mechanics.

PT symmetry applications span multiple physics disciplines.

Abstract

It is generally assumed that a Hamiltonian for a physically acceptable quantum system (one that has a positive-definite spectrum and obeys the requirement of unitarity) must be Hermitian. However, a PT-symmetric Hamiltonian can also define a physically acceptable quantum-mechanical system even if the Hamiltonian is not Hermitian. The study of PT-symmetric quantum systems is a young and extremely active research area in both theoretical and experimental physics. The purpose of this Review is to provide established scientists as well as graduate students with a compact, easy-to-read introduction to this field that will enable them to understand more advanced publications and to begin their own theoretical or experimental research activity. The ideas and techniques of PT symmetry have been applied in the context of many different branches of physics. This Review introduces the concepts of PT symmetry by focusing on elementary one-dimensional PT-symmetric quantum and classical mechanics and relies in particular on oscillator models to illustrate and explain the basic properties of PT-symmetric quantum theory.