Reply to Comment on "A no-go result for the quantum damped harmonic oscillator"

TL;DR

This paper refutes a recent claim about the quantum damped harmonic oscillator's vacuum state, clarifying the mistake and providing a simple example to illustrate the core issue.

Contribution

It corrects a misinterpretation in recent literature by demonstrating the incorrectness of the claimed vacuum state and clarifies the underlying problem.

Findings

Deguchi and Fujiwara's vacuum claim is incorrect

The supposed vacuum state is not truly a vacuum

A simple example clarifies the core issue

Abstract

In a recent paper, \cite{deguchi}, Deguchi and Fujiwara claim that our results in \cite{BGR} are wrong, and compute what they claim is the square integrable vacuum of their annihilation operators. In this brief note, we show that their vacuum is indeed not a vacuum, and we try to explain what is behind their mistake. We also consider a very simple example clarifying the core of the problem.