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- W2092379412 abstract "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." @default.
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- W2092379412 date "2009-12-01" @default.
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- W2092379412 title "Minimal position-velocity uncertainty wave packets in relativistic and non-relativistic quantum mechanics" @default.
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- W2092379412 doi "https://doi.org/10.1016/j.aop.2009.09.001" @default.
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