A no-go result for the quantum damped harmonic oscillator

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Abstract

In this letter we show that it is not possible to set up a canonical quantization for the damped harmonic oscillator using the Bateman Lagrangian. In particular, we prove that no square integrable vacuum exists for the natural ladder operators of the system, and that the only vacua can be found as distributions. This implies that the procedure proposed by some authors is only formally correct, and requires a much deeper analysis to be made rigorous.
Lingua originaleEnglish
pagine (da-a)2836-2838
Numero di pagine3
RivistaPHYSICS LETTERS A
Volume383
Stato di pubblicazionePublished - 2019

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ladders
harmonic oscillators
operators
vacuum

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy(all)

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title = "A no-go result for the quantum damped harmonic oscillator",
abstract = "In this letter we show that it is not possible to set up a canonical quantization for the damped harmonic oscillator using the Bateman Lagrangian. In particular, we prove that no square integrable vacuum exists for the natural ladder operators of the system, and that the only vacua can be found as distributions. This implies that the procedure proposed by some authors is only formally correct, and requires a much deeper analysis to be made rigorous.",
keywords = "Pseudo-bosons, Quantum damped harmonic oscillator",
author = "Federico Roccati and Francesco Gargano and Fabio Bagarello and Bagarello",
year = "2019",
language = "English",
volume = "383",
pages = "2836--2838",
journal = "Physics Letters, Section A: General, Atomic and Solid State Physics",
issn = "0375-9601",
publisher = "Elsevier",

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TY - JOUR

T1 - A no-go result for the quantum damped harmonic oscillator

AU - Roccati, Federico

AU - Gargano, Francesco

AU - Bagarello, Fabio

AU - Bagarello, null

PY - 2019

Y1 - 2019

N2 - In this letter we show that it is not possible to set up a canonical quantization for the damped harmonic oscillator using the Bateman Lagrangian. In particular, we prove that no square integrable vacuum exists for the natural ladder operators of the system, and that the only vacua can be found as distributions. This implies that the procedure proposed by some authors is only formally correct, and requires a much deeper analysis to be made rigorous.

AB - In this letter we show that it is not possible to set up a canonical quantization for the damped harmonic oscillator using the Bateman Lagrangian. In particular, we prove that no square integrable vacuum exists for the natural ladder operators of the system, and that the only vacua can be found as distributions. This implies that the procedure proposed by some authors is only formally correct, and requires a much deeper analysis to be made rigorous.

KW - Pseudo-bosons

KW - Quantum damped harmonic oscillator

UR - http://hdl.handle.net/10447/367729

M3 - Article

VL - 383

SP - 2836

EP - 2838

JO - Physics Letters, Section A: General, Atomic and Solid State Physics

JF - Physics Letters, Section A: General, Atomic and Solid State Physics

SN - 0375-9601

ER -