Metric Operators for Quasi-Hermitian Hamiltonians and Symmetries of Equivalent Hermitian Hamiltonians

TL;DR

This paper proves that diagonalizable operators with real spectra are quasi-Hermitian and explores how metric operators relate to symmetry generators of equivalent Hermitian Hamiltonians.

Contribution

It provides a simple proof of the quasi-Hermiticity of certain operators and clarifies the relationship between metric operators and symmetries of Hermitian counterparts.

Findings

Diagonalizable operators with real spectra are quasi-Hermitian

Metric operators are connected to symmetry generators of Hermitian Hamiltonians

The paper offers a straightforward proof of quasi-Hermiticity

Abstract

We give a simple proof of the fact that every diagonalizable operator that has a real spectrum is quasi-Hermitian and show how the metric operators associated with a quasi-Hermitian Hamiltonian are related to the symmetry generators of an equivalent Hermitian Hamiltonian.