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Dynamical invariants and quantization of the one-dimensional time-dependent, damped, and driven harmonic oscillator
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  • M. C. Bertin,
  • J. R. B. Peleteiro,
  • B. M. Pimentel,
  • J. A. Ramirez
M. C. Bertin
Instituto de Física, Universidade Federal da Bahia
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J. R. B. Peleteiro
Instituto de Física, Universidade Federal da Bahia
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B. M. Pimentel
Instituto de Física Teórica, São Paulo State University
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J. A. Ramirez
Instituto de Física, Universidade Federal da Bahia
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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.
Keywords: Dynamical Invariants; Quantum Damped Oscillator; Time-Dependent Systems; Dissipative Systems.