  Delay times in quantum mechanics always represented an intriguing challenge
for physicists. Due to the fact that quantum mechanical experiments are, often,
hard to be implemented, the possibility to connect delay times with laser
lateral displacements gives us the opportunity to prepare, in optical
laboratories, experiments which are equivalent to the quantum mechanical ones
in detecting delay times. In this article, we will show in detail not only the
relationship between delay times and Goos-Haenchen shifts, but also the close
connection between the impulse change in quantum mechanics and angular
deviations in optics. Lateral shifts are caused by the phase of Fresnel
coefficients whereas angular deviations by the breaking of symmetry of the wave
number distributions. The classical formula for the delay time is based on the
use of the stationary phase method and contains a divergence for incidence at a
critical potential energy. For Gaussian beams, the mean value calculation
removes such a divergence. The closed expression for the delay time for
incidence at critical energy show an excellent agreement with the numerical
calculation. The three-dimensional analysis of delay times allow to find the
final and definitive connection between wave packets reflected by a potential
in quantum mechanics and optical beams reflected by a dielectric/air interface.
