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.
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