  We illustrate the correspondence between the quantum Interaction
Picture-evolution of the state of a quantum system in Hilbert space and a
combination of local and global transformations of its Wigner function in phase
space. To this aim, we consider the time-evolution of a quantized harmonic
oscillator driven by both a linear and a quadratic (in terms of bosonic
creation and annihilation operators) potentials and employ the Magnus series to
derive the exact form of the time-evolution operator. In this case, the
Interaction Picture corresponds to a local transformation of phase
space-reference frame into the one that is co-moving with the Wigner function.
