Bateman Oscillators: Caldirola-Kanai and Null Lagrangians and Gauge Functions

TL;DR

This paper develops a Lagrangian formalism for Bateman oscillators, introduces methods to derive Caldirola-Kanai and null Lagrangians, and explores gauge functions to transform undriven into driven oscillators, with implications for quantization.

Contribution

It presents a novel approach to derive Lagrangians for Bateman oscillators and uses gauge functions to connect undriven and driven systems, advancing their quantization.

Findings

Derived Caldirola-Kanai and null Lagrangians for Bateman oscillators

Obtained gauge functions to convert undriven into driven oscillators

Discussed implications for quantization of these systems

Abstract

The Lagrange formalism is developed for Bateman oscillators, which include both damped and amplified systems, and a novel method to derive the Caldirola-Kanai and null Lagrangians is presented. For the null Lagrangians, corresponding gauge functions are obtained. It is shown that the gauge functions can be used to convert the undriven Bateman oscillators into the driven ones. Applications of the obtained results to quantizatation of the Bateman oscillators are briefly discussed.