For the nerrow wave packet of a partical
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The concept of wave packet has undergone many, more or less subtle, variations during the last 100 years. Sure, interference is important, but it is not all. The common motive is that when a system admits a continuous band of wave solutions (classical or quantum, it does not really matter), its dynamics can exhibit localized-interference features that behave differently from the individual waves. They appear as persistent "objects" with strikingly different properties than those of the waves that compose them (for example, their apparent collective - or "group" - velocities can be quite different). Examples are vortices, maelstroems and tsunamis in hydrodynamics and, why not, particles and "resonances" in subatomic physics. The concept is nice, interesting, and probably contains a lot of truth, though it need not be strictly applicable to all the situations where it was tried. In any case, any kind of wave equation (be it Schroedinger or other) leads to this kind of discussions.
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