Editing Wave packet (section)

=== Wave packets and the classical limit ===
Schrodinger developed wave packets in hopes of interpreting quantum wave solutions as locally compact wave groups.<ref name="Kragh"/> Such packets tradeoff position localization for spreading momentum. In the coordinate representation of the wave (such as the [[Cartesian coordinate system]]), the position of the particle's localized probability is specified by the position of the packet solution.  The narrower the spatial wave packet, and therefore the better localized the position of the wave packet, the larger the spread in the [[momentum]] of the wave. This trade-off between spread in position and spread in momentum is a characteristic feature of the Heisenberg uncertainty principle.

One kind of optimal tradeoff minimizes the product of position uncertainty <math>\Delta x</math> and momentum uncertainty <math>\Delta p_x</math>.<ref name="Schiff">{{Cite book |last=Schiff |first=Leonard I. |title=Quantum mechanics |date=1995 |publisher=McGraw-Hill |isbn=978-0-07-055287-6 |edition=3. ed., 29. print |series=International series in pure and applied physics |location=New York}}</ref>{{rp|60}} If we place such a packet at rest it stays at rest: the average value of the position and momentum match a classical particle. However it spreads out in all directions with a velocity given by the optimal momentum uncertainty <math>\Delta p_x</math>. The spread is so fast that in the distance of once around an atom the wave packet is unrecognizable.