  We review some recent results obtained for the time evolution of wave packets
for systems of equations of pseudo-differential type, including Schr{\"o}dinger
ones, and discuss their application to the approximation of the associated
unitary propagator. We start with scalar equations, propagation of coherent
states, and applications to the Herman-Kluk approximation. Then we discuss the
extension of these results to systems with eigenvalues of constant multiplicity
or with smooth crossings.

Analysis of PDEs