  We provide a new canonical approach for studying the quantum mechanical
damped harmonic oscillator based on the doubling of degrees of freedom
approach. Explicit expressions for Lagrangians of the elementary modes of the
problem, characterising both forward and backward time propagations are given.
  A Hamiltonian analysis, showing the equivalence with the Lagrangian approach,
is also done. Based on this Hamiltonian analysis, the quantization of the model
is discussed.
