Non-Hermitian Hamiltonians with real and complex eigenvalues in a Lie-algebraic framework

TL;DR

This paper introduces a Lie-algebraic approach to analyze non-Hermitian Hamiltonians, revealing how their eigenvalues transition from real to complex, and discusses their pseudo-Hermiticity properties.

Contribution

It presents a novel Lie-algebraic framework using complex Lie algebras to study eigenvalue transitions in non-Hermitian Hamiltonians.

Findings

Lie algebraic methods elucidate eigenvalue transitions

Characterization of pseudo-Hermiticity in these Hamiltonians

Application to complexified quantum models

Abstract

We show that complex Lie algebras (in particular sl(2,C)) provide us with an elegant method for studying the transition from real to complex eigenvalues of a class of non-Hermitian Hamiltonians: complexified Scarf II, generalized P\"oschl-Teller, and Morse. The characterizations of these Hamiltonians under the so-called pseudo-Hermiticity are also discussed.