Availability of short, femtosecond laser pulses has recently made feasible
the probing of phases in an atomic or molecular wave-packet (superposition
of energy eigenstates). With short duration excitations the initial form of
the wave-packet is an essentially real "doorway state," and this develops
phases for each of its component amplitudes as it evolves. It is suggested
that these phases are hallmarks of a time arrow and irreversibility that ar
e inherent in the quantum mechanical processes of preparation and evolution
. To display the non-triviality of the result, we show under what condition
s it would not hold; to discuss its truth, we consider some apparent contra
dictions. We propose that (in time-reversal invariant systems) the preparat
ion of "initially" complex wave-packets needs finite times to complete, i.e
., is not instantaneous.