Dynamical invariants and quantization of the one-dimensional time-dependent, damped, and driven harmonic oscillator

TL;DR

This paper introduces a novel quantization method for a one-dimensional harmonic oscillator with time-dependent parameters, utilizing dynamical invariants to address the complexities introduced by damping and driving forces.

Contribution

It presents a new quantization procedure based on dynamical invariants specifically tailored for oscillators with time-dependent frequency, damping, and forcing.

Findings

Developed a quantization framework using linear invariants.

Applied the method to oscillators with varying parameters.

Provided insights into the quantum behavior of dissipative systems.

Abstract

In this paper, it is proposed a quantization procedure for the one-dimensional harmonic oscillator with time-dependent frequency, time-dependent driven force, and time-dependent dissipative term. The method is based on the construction of dynamical invariants previously proposed by the authors, in which fundamental importance is given to the linear invariants of the oscillator.