Comment on "the quantum dynamics for general time-dependent three coupled oscillators"

TL;DR

This paper critiques a recent approach to analyzing quantum dynamics in three coupled oscillators, highlighting errors in the decoupling method and suggesting the need for alternative strategies.

Contribution

It identifies flaws in the previous decoupling method and discusses potential alternative approaches for analyzing quantum dynamics in coupled oscillators.

Findings

The claimed decoupling of oscillators is incorrect.

The unitary transformation approach used is flawed.

Alternative methods are necessary for accurate analysis.

Abstract

In a recent paper, Hassoul et al.[1], the authors proposed an analysis of the quantum dynamics for general time-dependent three coupled oscillators through an approach based on their decouplement using the unitary transformation method. Thus, to diagonalize the transformed Hamiltonian, they introduce a new unitary operator corresponding to a three-dimensional rotation parameterized by Euler angles. Through this procedure, Hassoul et al. [1] claim that the coupled oscillatory subsystems are completely decoupled. This last approach is partly wrong. In this brief note, we show that their method is indeed not correct and we try to explain what truly lies behind their mistakes. We also propose a brief discussion on an alternative method that might achieve satisfactory results.