  We formulate analytically the reflection of a one dimensional, expanding free
wave-packet (wp) from an infinite barrier. Three types of wp's are considered,
representing an electron, a molecule and a classical object. We derive a
threshold criterion for the values of the dynamic parameters so that reciprocal
(Kramers-Kronig) relations hold {\it in the time domain} between the
log-modulus of the wp and the (analytic part of its) phase acquired during the
reflection. For an electron, in a typical case, the relations are shown to be
satisfied. For a molecule the modulus-phase relations take a more complicated
form, including the so called Blaschke term. For a classical particle
characterized by a large mean momentum ($\hbar K >> \frac{\hbar trajectory
length} {(size of wave-packet)^2} >>> \frac{\hbar}{size of wave-packet}$) the
rate of acquisition of the relative phase between different wp components is
enormous (for a bullet it is typically $10^{14}$ GHertz) with also a very large
value for the phase maximum.
