A no-go result for the quantum damped harmonic oscillator
Quantum Physics
2019-09-04 v2
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 {\em 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.
Cite
@article{arxiv.1906.05121,
title = {A no-go result for the quantum damped harmonic oscillator},
author = {Fabio Bagarello and Francesco Gargano and Federico Roccati},
journal= {arXiv preprint arXiv:1906.05121},
year = {2019}
}