A novel approach to the synthesis of nondispersive wave packet solutions to the Klein--Gordon and Dirac equations

Journal Article · Mon Oct 01 00:00:00 EDT 1990 · Journal of Mathematical Physics (New York); (USA)

DOI:https://doi.org/10.1063/1.528995· OSTI ID:6279390

Shaarawi, A M; Besieris, I M ^[1]; Ziolkowski, R W ^[2]

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1. The Bradley Department of Electrical Engineering, Virginia Polytechnic Institute and State University, Blacksburg, VA (USA)
2. Engineering Research Division, Lawrence Livermore National Laboratory, Livermore, CA (USA)

A systematic approach to the derivation of exact nondispersive packet solutions to equations modeling relativistic massive particles is introduced. It is based on a novel bidirectional representation used to synthesize localized Brittingham-like solutions to the wave and Maxwell's equations. The theory is applied first to the Klein--Gordon equation; the resulting nondispersive solutions can be used as de Broglie wave packets representing localized massive scalar particles. The resemblance of such solutions to previously reported nondispersive wave packets is discussed and certain subtle aspects of the latter, especially those arising in connection to the correct choice of dispersion relationships and the definition of group velocity, are clarified. The results obtained for the Klein--Gordon equation are also used to provide nondispersive solutions to the Dirac equation which models spin 1/2 massive fermions.

• DOE Contract Number: W-7405-ENG-48
• OSTI ID: 6279390
• Journal Information: Journal of Mathematical Physics (New York); (USA), Journal Name: Journal of Mathematical Physics (New York); (USA) Vol. 31:10; ISSN 0022-2488; ISSN JMAPA
• Country of Publication: United States
• Language: English

Related Subjects

645400* -- High Energy Physics-- Field Theory
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
CHARGED PARTICLES
CORRELATIONS
DE BROGLIE WAVELENGTH
DIFFERENTIAL EQUATIONS
DIRAC EQUATION
DISPERSION RELATIONS
EQUATIONS
KLEIN-GORDON EQUATION
MASS
MAXWELL EQUATIONS
NONLINEAR PROBLEMS
PARTIAL DIFFERENTIAL EQUATIONS
REST MASS
SCALAR FIELDS
WAVE EQUATIONS
WAVE PACKETS