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arXiv · 1906.05121

A no-go result for the quantum damped harmonic oscillator

Fabio Bagarello·Francesco Gargano·Federico Roccati
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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.

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Fabio Bagarello, Francesco Gargano, Federico Roccati. 2019-06-14. A no-go result for the quantum damped harmonic oscillator. https://doi.org/10.1016/j.physleta.2019.06.022

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