A new approach to the quantization the damped harmonic oscillator

Matthew J. Blacker, David L. Tilbrook

Published 2021-07-13Version 1

In this paper, a new approach for constructing Lagrangians for driven and undriven linearly damped systems is proposed, by introducing a redefined time coordinate and an associated coordinate transformation to ensure that the resulting Lagrangian satisfies the Helmholtz conditions. The approach is applied to canonically quantize the damped harmonic oscillator and it predicts an energy spectrum that decays at a different rate to previous models, and a different critical damping point for the quantized system, which determines transitions between energy eigenstates. It is also demonstrated how to apply the procedure to a driven damped harmonic oscillator.