Pseudo-Hermiticity versus PT-Symmetry II: A complete characterizatio n of non-Hermitian Hamiltonians with a real spectrum

TL;DR

This paper provides a comprehensive criterion to determine when non-Hermitian Hamiltonians have real spectra, focusing on pseudo-Hermiticity and PT-symmetry, crucial for quantum physics applications.

Contribution

It offers a complete characterization of non-Hermitian Hamiltonians with real spectra, advancing understanding of their spectral properties.

Findings

Established necessary and sufficient conditions for real spectra

Linked pseudo-Hermiticity to spectral reality

Clarified the role of biorthonormal eigenvectors

Abstract

We give a necessary and sufficient condition for the reality of the spectrum of a non-Hermitian Hamiltonian admitting a complete set of biorthonormal eigenvectors.