  Quantum states evolving at equidistant steps into a set of mutually
orthogonal states of finite or infinite cardinality p exhibit an interesting
physical effect. The analysis of the amplitudes of the state at half the step
time with the elements of this set (the anticipation amplitudes) shows, that
for randomly chosen states measurements of the state at half-step time reveal
information about the states at full step time, anticipating future states and
reflecting past states with significant probability. For fixed N and p to
infinity, the probability to measure a state which is N steps apart in future
or past exceeds a constant lower bound. We characterize the spectrum, establish
an analog to Plack's relation, define a random sampling scheme, analyze the
resulting distribution of the anticipation probabilities and point out
applications.
