Misbelief and misunderstandings on the non--Markovian dynamics of a damped harmonic oscillator

We use the exact solution for the damped harmonic oscillator to discuss some relevant aspects of its open dynamics are often misunderstood. We compare two different approximations both referred to as a rotating wave approximation. Using a specific example, we clarify some issues related to non-Markovian dynamics, non-Lindblad-type dynamics, and positivity of the density matrix.