Quantization of the Damped Harmonic Oscillator Revisited

TL;DR

This paper revisits quantum models of the damped harmonic oscillator, comparing existing and new approaches, and shows their local equivalence with improved high-energy behavior and connections to open quantum systems.

Contribution

It demonstrates the local equivalence between two quantum models of damping and highlights the advantages of a newer model over traditional ones.

Findings

The two models are locally equivalent.

The new model exhibits better high-energy behavior.

It aligns well with open quantum systems approaches.

Abstract

We return to the description of the damped harmonic oscillator by means of a closed quantum theory with a general assessment of previous works, in particular the Bateman-Caldirola-Kanai model and a new model recently proposed by one of the authors. We show the local equivalence between the two models and argue that latter has better high energy behavior and is naturally connected to existing open-quantum-systems approaches.