Alternative approach to the quantization of the damped harmonic oscillator

In this paper, a new approach for constructing Lagrangians driven and undriven linearly damped systems is proposed, by introducing redefined time coordinate an associated transformation to ensure that the resulting Lagrangian satisfies Helmholtz conditions. The applied canonically quantize harmonic oscillator although it predicts energy spectrum decays at same rate previous models, unlike those approaches recovers classical critical damping condition, which determines transitions between eigenstates, therefore consistent with correspondence principle. It also demonstrated how apply procedure oscillator.