  We use the semiclassical method proposed in \cite{Adelcio2003} to study
scalar products such as the overlap, Husimi functions and fidelity decay. Scars
of classical periodic orbits arise naturally in this pertubative expansion. We
also derive analytically a well known numerical result that fidelity has a
quadratic decay for short times. We study the overlap in the chaotic regime and
integrable for some simple systems.
