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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Data di pubblicazione: 2019
Titolo: A no-go result for the quantum damped harmonic oscillator
Autori: 
BAGARELLO, Fabio (Corresponding)
GARGANO, Francesco
ROCCATI, Federico
Citazione: Bagarello, F., Gargano, F., & Roccati, F. (2019). A no-go result for the quantum damped harmonic oscillator. PHYSICS LETTERS A, 383(24), 2836-2838.
Rivista: 
PHYSICS LETTERS A  
Digital Object Identifier (DOI): 10.1016/j.physleta.2019.06.022
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.
Settore Scientifico Disciplinare: Settore MAT/07 - Fisica Matematica
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Utilizza questo identificativo per citare o creare un link a questo documento:
http://hdl.handle.net/10447/367729
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