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].
Data di pubblicazione: | 2019 | |
Titolo: | A no-go result for the quantum damped harmonic oscillator | |
Autori: | ||
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 [10.1016/j.physleta.2019.06.022]. | |
Rivista: | ||
Digital Object Identifier (DOI): | http://dx.doi.org/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 | |
Appare nelle tipologie: | 1.01 Articolo in rivista |
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