Time-dependent coupled harmonic oscillators: Comment

TL;DR

This paper critiques a previous method for solving time-dependent coupled harmonic oscillators, identifying errors in the elimination of time-dependent masses and providing a correct approach.

Contribution

It corrects the previous method by properly eliminating time-dependent masses in the Hamiltonian of coupled oscillators.

Findings

The original method contains inaccuracies in removing time-dependent masses.

A corrected procedure for eliminating time-dependent masses is proposed.

The revised approach ensures accurate Hamiltonian transformation.

Abstract

Macedo and Guedes showed recently how to solve a system of coupled harmonic oscillators with time dependent parameters [{ J. Math. Phys.} {\bf 53}, 052101 (2012)]. We show here that the way in which they get rid of the time dependent masses is incorrect and some terms lack in the transformed Hamiltonian. We also show a correct way of eliminating from the Hamiltonian the time dependent masses.