Physics
Scientific paper
Dec 2009
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2009anphy.324.2599a&link_type=abstract
Annals of Physics, Volume 324, Issue 12, p. 2599-2621.
Physics
Scientific paper
We consider wave packets of free particles with a general energy-momentum dispersion relation E(p). The spreading of the wave packet is determined by the velocity v=∂pE. The position-velocity uncertainty relation ΔxΔv⩾12|<∂p2E>| is saturated by minimal uncertainty wave packets Φ(p)=Aexp(-αE(p)+βp). In addition to the standard minimal Gaussian wave packets corresponding to the non-relativistic dispersion relation E(p)=p2/2m, analytic calculations are presented for the spreading of wave packets with minimal position-velocity uncertainty product for the lattice dispersion relation E(p)=-cos(pa)/ma2 as well as for the relativistic dispersion relation E(p)=p2+m2. The boost properties of moving relativistic wave packets as well as the propagation of wave packets in an expanding Universe are also discussed.
Al-Hashimi M. H.
Wiese Uwe-Jens
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