Dynamical Invariants and Quantization of the One-Dimensional Time-Dependent, Damped, and Driven Harmonic Oscillator

Abstract

In this paper, it is proposed a quantization procedure for the one-dimensional harmonic oscillator with time-dependent frequency, time-dependent driven force, and time-dependent dissipative term. The method is based on the construction of dynamical invariants previously proposed by the authors, in which fundamental importance is given to the linear invariants of the oscillator.

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Funding

This study was financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior – Brasil (CAPES) – Finance Code 001, and in part by the Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq).

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Correspondence to M. C. Bertin.

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Bertin, M.C., Peleteiro, J.R.B., Pimentel, B.M. et al. Dynamical Invariants and Quantization of the One-Dimensional Time-Dependent, Damped, and Driven Harmonic Oscillator. Braz J Phys (2020). https://doi.org/10.1007/s13538-020-00765-8

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Keywords

  • Dynamical invariants
  • Dissipative systems
  • Quantum damped oscillator
  • Time-dependent systems