TY - JOUR
T1 - A no-go result for the quantum damped harmonic oscillator
AU - Bagarello, Fabio
AU - Gargano, Francesco
AU - Roccati, Federico
AU - Bagarello, null
PY - 2019
Y1 - 2019
N2 - 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.
AB - 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.
KW - Pseudo-bosons
KW - Quantum damped harmonic oscillator
KW - Pseudo-bosons
KW - Quantum damped harmonic oscillator
UR - http://hdl.handle.net/10447/367729
M3 - Article
SN - 0375-9601
VL - 383
SP - 2836
EP - 2838
JO - Physics Letters, Section A: General, Atomic and Solid State Physics
JF - Physics Letters, Section A: General, Atomic and Solid State Physics
ER -