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

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