  Quantization of the damped harmonic oscillator is taken as leitmotiv to
gently introduce elements of quantum probability theory for physicists. To this
end, we take (graduate) students in physics as entry level and explain the
physical intuition and motivation behind the, sometimes overwhelming, math
machinery of quantum probability theory.
  The main text starts with the quantization of the (undamped) harmonic
oscillator from the Heisenberg and Schroedinger point of view. We show how both
treatments are special instances of a quantum probabilistic quantization
procedure: the second quantization functor. We then apply the second
quantization functor to the damped harmonic oscillator and interpret the
quantum dynamics of the position and energy operator as stochastic processes.
