6533b830fe1ef96bd12971b6

RESEARCH PRODUCT

A no-go result for the quantum damped harmonic oscillator

F. RoccatiFabio BagarelloFrancesco Gargano

subject

Pseudo-bosonPhysicsQuantum PhysicsCanonical quantizationFOS: Physical sciencesGeneral Physics and Astronomy01 natural sciences010305 fluids & plasmasSet (abstract data type)Quantum damped harmonic oscillatorsymbols.namesakeClassical mechanicsLadder operatorSquare-integrable functionGo/no go0103 physical sciencessymbolsQuantum Physics (quant-ph)010306 general physicsSettore MAT/07 - Fisica MatematicaQuantumLagrangianHarmonic oscillator

description

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.

yearjournalcountryeditionlanguage
2019-01-01Physics Letters A
https://doi.org/10.1016/j.physleta.2019.06.022