Solution of the Schroedinger equation for a system excited by a time Dirac pulse of potential. An example of the connection with the classical limit through a particular smoothing of the Wigner function

The authors show for a simple problem where analytical calculations can be performed, the time evolution of the wavefunction describes the motion in phase space, first through the time evolution of a density pulse and secondly by considering the Wigner distribution function. In the classical limit this last distribution exhibits a very complex physically meaningless structure but by smoothing with a double gaussian kernel, the correct limit is obtained.