A no-go result for the quantum damped harmonic oscillator

Research output: Contribution to journalArticle

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.
Original languageEnglish
Pages (from-to)2836-2838
Number of pages3
JournalPHYSICS LETTERS A
Volume383
Publication statusPublished - 2019

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ladders
harmonic oscillators
operators
vacuum

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy(all)

Cite this

A no-go result for the quantum damped harmonic oscillator. / Gargano, Francesco; Roccati, Federico; Bagarello, Fabio; Bagarello.

In: PHYSICS LETTERS A, Vol. 383, 2019, p. 2836-2838.

Research output: Contribution to journalArticle

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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.

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KW - Quantum damped harmonic oscillator

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

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