Minimal positionvelocity uncertainty wave packets in relativistic and nonrelativistic quantum mechanics
Abstract
We consider wave packets of free particles with a general energymomentum dispersion relation E(p). The spreading of the wave packet is determined by the velocity v={partial_derivative}{sub p}E. The positionvelocity uncertainty relation {delta}x{delta}v{>=}1/2 <{partial_derivative}{sub p}{sup 2}E> is saturated by minimal uncertainty wave packets {phi}(p)=Aexp({alpha}E(p)+{beta}p). In addition to the standard minimal Gaussian wave packets corresponding to the nonrelativistic dispersion relation E(p)=p{sup 2}/2m, analytic calculations are presented for the spreading of wave packets with minimal positionvelocity uncertainty product for the lattice dispersion relation E(p)=cos(pa)/ma{sup 2} as well as for the relativistic dispersion relation E(p)={radical}(p{sup 2}+m{sup 2}). The boost properties of moving relativistic wave packets as well as the propagation of wave packets in an expanding Universe are also discussed.
 Authors:

 Albert Einstein Center for Fundamental Physics, Institute for Theoretical Physics, Bern University, Sidlerstrasse 5, CH3012 Bern (Switzerland)
 Publication Date:
 OSTI Identifier:
 21336078
 Resource Type:
 Journal Article
 Journal Name:
 Annals of Physics (New York)
 Additional Journal Information:
 Journal Volume: 324; Journal Issue: 12; Other Information: DOI: 10.1016/j.aop.2009.09.001; PII: S00034916(09)001663; Copyright (c) 2009 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 00034916
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; DISPERSION RELATIONS; MASS; QUANTUM MECHANICS; RELATIVISTIC RANGE; UNIVERSE; VELOCITY; WAVE PACKETS
Citation Formats
AlHashimi, M.H., and Wiese, U J. Minimal positionvelocity uncertainty wave packets in relativistic and nonrelativistic quantum mechanics. United States: N. p., 2009.
Web. doi:10.1016/j.aop.2009.09.001.
AlHashimi, M.H., & Wiese, U J. Minimal positionvelocity uncertainty wave packets in relativistic and nonrelativistic quantum mechanics. United States. doi:10.1016/j.aop.2009.09.001.
AlHashimi, M.H., and Wiese, U J. Tue .
"Minimal positionvelocity uncertainty wave packets in relativistic and nonrelativistic quantum mechanics". United States. doi:10.1016/j.aop.2009.09.001.
@article{osti_21336078,
title = {Minimal positionvelocity uncertainty wave packets in relativistic and nonrelativistic quantum mechanics},
author = {AlHashimi, M.H. and Wiese, U J},
abstractNote = {We consider wave packets of free particles with a general energymomentum dispersion relation E(p). The spreading of the wave packet is determined by the velocity v={partial_derivative}{sub p}E. The positionvelocity uncertainty relation {delta}x{delta}v{>=}1/2 <{partial_derivative}{sub p}{sup 2}E> is saturated by minimal uncertainty wave packets {phi}(p)=Aexp({alpha}E(p)+{beta}p). In addition to the standard minimal Gaussian wave packets corresponding to the nonrelativistic dispersion relation E(p)=p{sup 2}/2m, analytic calculations are presented for the spreading of wave packets with minimal positionvelocity uncertainty product for the lattice dispersion relation E(p)=cos(pa)/ma{sup 2} as well as for the relativistic dispersion relation E(p)={radical}(p{sup 2}+m{sup 2}). The boost properties of moving relativistic wave packets as well as the propagation of wave packets in an expanding Universe are also discussed.},
doi = {10.1016/j.aop.2009.09.001},
journal = {Annals of Physics (New York)},
issn = {00034916},
number = 12,
volume = 324,
place = {United States},
year = {2009},
month = {12}
}