  We consider the evolution, for a time-dependent Schr\"odinger equation, of
the so called Dirac comb. We show how this evolution allows us to recover
explicitly (indeed optically) the values of the quadratic generalized Gauss
sums. Moreover we use the phenomenon of superoscillatory sequences to prove
that such Gauss sums can be asymptotically recovered from the values of the
spectrum of any sufficiently regular function compactly supported on $\R$. The
fundamental tool we use is the so called Galilean transform that was introduced
and studied in the context on non-linear time dependent Schr\"odinger
equations. Furthermore, we utilize this tool to understand in detail the
evolution of an exponential $e^{i\omega x}$ in the case of a Schr\"odinger
equation with time-independent periodic potential.
