# Comment on "Quantization of the damped harmonic oscillator" [Serhan et al, J. Math. Phys. 59, 082105 (2018)]

## TL;DR

This paper critiques a recent work on quantizing the damped harmonic oscillator, emphasizing the importance of non-Hermiticity in the Hamiltonian as a key quantum signature of dissipation.

## Contribution

It highlights the oversight of non-Hermiticity in the previous Hamiltonian construction, clarifying its role in representing dissipation in quantum systems.

## Key findings

- The Hamiltonian in the criticized paper is non-Hermitian.
- Real eigenvalues claimed in the paper are actually complex.
- Non-Hermiticity is essential for capturing dissipation quantum mechanically.

## Abstract

A recent paper [J. Math. Phys. {\bf 59}, 082105 (2018)] constructs a Hamiltonian for the (dissipative) damped harmonic oscillator. We point out that non-Hermiticity of this Hamiltonian has been ignored to find real discrete eigenvalues which are actually non-real. We emphasize that non-Hermiticity in Hamiltonian is crucial and it is a quantal signature of dissipation.