Some remarks on few recent results on the damped quantum harmonic oscillator

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Abstract

In a recent paper, Deguchi et al. (2019), the authors proposed an analysis of the damped quantum harmonic oscillator in terms of ladder operators. This approach was shown to be partly incorrect in Bagarello et al. (2019), via a simple no-go theorem. More recently, (Deguchi and Fujiwara, 2019), Deguchi and Fujiwara claimed that our results in Bagarello et al. (2019) 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 mistakes in Deguchi et al. (2019) and Deguchi and Fujiwara (2019). We also propose a very simple example clarifying the core of the problem.
Lingua originaleEnglish
pagine (da-a)168091-
Numero di pagine6
RivistaAnnals of Physics
Volume414
Stato di pubblicazionePublished - 2020

All Science Journal Classification (ASJC) codes

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