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.

Bagarello F., Gargano F., Roccati F. (2019). A no-go result for the quantum damped harmonic oscillator. PHYSICS LETTERS A, 383(24), 2836-2838 [10.1016/j.physleta.2019.06.022].

A no-go result for the quantum damped harmonic oscillator

Bagarello F.
;
Gargano F.;Roccati F.
2019-01-01

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.
2019
Settore MAT/07 - Fisica Matematica
Bagarello F., Gargano F., Roccati F. (2019). A no-go result for the quantum damped harmonic oscillator. PHYSICS LETTERS A, 383(24), 2836-2838 [10.1016/j.physleta.2019.06.022].
File in questo prodotto:
File Dimensione Formato  
anogoresult.pdf

Open Access dal 25/08/2020

Tipologia: Post-print
Dimensione 112.89 kB
Formato Adobe PDF
112.89 kB Adobe PDF Visualizza/Apri
1-s2.0-S0375960119305572-main.pdf

Solo gestori archvio

Descrizione: pdf
Tipologia: Versione Editoriale
Dimensione 226.15 kB
Formato Adobe PDF
226.15 kB Adobe PDF   Visualizza/Apri   Richiedi una copia

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10447/367729
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 13
  • ???jsp.display-item.citation.isi??? 9
social impact