  In this paper we numerically solve the time dependent Schr\"odinger equation
for scenarios using wave packets. These examples include the free wave packet,
which we use to show the difference between group and phase velocities, the
packet in a harmonic oscillator potential with non-trivial initial conditions
in one and two dimensions, which is compared with their classical analogs to
show how Ehrenfest theorem holds. We also include simulations of the
diffraction through the single and double slit potentials, the refraction with
a step potential and the dispersion by a central potential. The aim of this
paper is to illustrate with simulations, nowadays easy to implement, scenarios
that can help explaining the basics of the wave-particle duality.
