Time arrow in wave-packet evolution

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 are inherent in the quantum mechanical processes of preparation and evolution. To display the non-triviality of the result, we show under what conditions it would not hold; to discuss its truth, we consider some apparent contradictions. We propose that (in time-reversal invariant systems) the preparation of "initially" complex wave-packets needs finite times to complete, i.e., is not instantaneous.