The Interpretation of Quantum-Mechanical Models with Non-Hermitian Hamiltonians and Real Spectra

TL;DR

This paper develops a framework for interpreting quantum models with non-Hermitian Hamiltonians that have real spectra, ensuring proper physical observable definitions and analyzing specific examples.

Contribution

It introduces a general approach to interpret non-Hermitian Hamiltonians with real spectra using Hermitian Hamiltonians in standard Hilbert space, clarifying observable algebra.

Findings

Established a consistent interpretation scheme for non-Hermitian models

Analyzed models by Cannata et al. and Hatano and Nelson within this framework

Highlighted the importance of correct observable definitions in such systems

Abstract

We study the quantum-mechanical interpretation of models with non-Hermitian Hamiltonians and real spectra. We set up a general framework for the analysis of such systems in terms of Hermitian Hamiltonians defined in the usual Hilbert space $L_2(-\infty,\infty)$. Special emphasis is put on the correct definition of the algebra of physical observables. Within this scheme we consider various examples, including the model recently introduced by Cannata et al. and the model of Hatano and Nelson.