  This work represents a first systematic attempt to create a common ground for
semi-classical and time-frequency analysis. These two different areas combined
together provide interesting outcomes in terms of Schr\"odinger type equations.
Indeed, continuity results of both Schr\"odinger propagators and their
asymptotic solutions are obtained on $\hbar$-dependent Banach spaces, the
semi-classical version of the well-known modulation spaces. Moreover, their
operator norm is controlled by a constant independent of the Planck's constant
$\hbar$. The main tool in our investigation is the joint application of
standard approximation techniques from semi-classical analysis and a
generalized version of Gabor frames, dependent of the parameter $\hbar$.
Continuity properties of more general Fourier integral operators (FIOs) and
their sparsity are also investigated.
