Abstract
We discuss four general features of the force-free evolution of wave packets: (1) The spatial spread of a packet changes with time in a simple way. (2) For sufficiently short durations (related to the spread in the momentum of the packet) the probability distribution will move with uniform speed and little change in shape. (3) After a sufficiently long time (related to the initial spatial spread) the wave function converges to a simple form that is simply related to the momentum distribution of the packet. In this asymptotic regime the shape of the probability distribution no longer changes, and its scale increases linearly with the time. (4) There is an infinite denumerable set of simple wave packets (the Hermite-Gauss packets) that do not change shape at any time during their evolution.
| Original language | English |
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| Pages (from-to) | 1102-1107 |
| Number of pages | 6 |
| Journal | American Journal of Physics |
| Volume | 76 |
| Issue number | 12 |
| DOIs | |
| Publication status | Published - 2008 |