Comment on Demystifying the constancy of the Ermakov-Lewis invariant for a time-dependent oscillator

TL;DR

This paper demonstrates that a slight change to Padmanabhan's Lagrangian yields the most general dynamical invariant for a time-dependent oscillator, clarifying the invariance properties discussed in prior work.

Contribution

It introduces a simple modification to existing Lagrangian formulations to derive the most general dynamical invariant for time-dependent oscillators.

Findings

Modified Lagrangian produces the general invariant.

Clarifies the invariance properties of the oscillator.

Connects previous formulations to a unified invariant.

Abstract

We show that a simple modification of the Lagrangian proposed by Padmanabhan in the paper [Mod. Phys. Lett. A 33, 1830005 (2018), arXiv:1712.07328] leads to the most general dynamical invariant in [Ray and Reid, Phys. Lett. A 71, 317 (1979)]