Comment on: "Quantum dynamics of a general time-dependent coupled oscillator"

TL;DR

This paper critiques a previous study on quantum dynamics of time-dependent coupled oscillators, identifying fundamental errors that invalidate the claimed results and conclusions.

Contribution

It provides a critical analysis revealing errors in the previous work's methodology and invalidates their claims about uncoupling and diagonalization of invariants.

Findings

Identifies basic errors in the previous analysis

Shows the claimed invariants are not valid

Concludes the results of the original study are incorrect

Abstract

By using dynamical invariants theory, Hassoul et al. [1,2] investigate the quantum dynamics of two (2D) and three (3D) dimensional time-dependent coupled oscillators. They claim that, in the 2D case, introducing two pairs of annihilation and creation operators uncouples the original invariant operator so that it becomes the one that describes two independent subsystems. For the 3D case, the authors pretend that they have obtained a diagonalized invariant which is exactly the sum of three simple harmonic oscillators. We show that their investigations suffer from basic errors and therefore the found results are not valid .