A new approach to the quantization of the damped harmonic oscillator

• URL: http://arxiv.org/abs/2107.05827v3
• Date: Thu, 15 Jul 2021 03:50:46 GMT
• Title: A new approach to the quantization of the damped harmonic oscillator
• Authors: Matthew J. Blacker, David L. Tilbrook
• Abstract summary: A new approach for constructing Lagrangians for driven and undriven linearly damped systems is proposed. A new time coordinate is introduced to ensure that the resulting Lagrangian satisfies the Helmholtz conditions.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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 although it predicts an energy spectrum that decays at the same rate to previous models, unlike those approaches it recovers the classical critical damping condition, which determines transitions between energy eigenstates, and is therefore consistent with the correspondence principle. It is also demonstrated how to apply the procedure to a driven damped harmonic oscillator.

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