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

Amr M. Shaarawi, Ioannis M. Besieris, Richard W Ziolkowski

Research output: Contribution to journalArticle

47 Citations (Scopus)

Abstract

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.

Original languageEnglish (US)
Pages (from-to)2511-2519
Number of pages9
JournalJournal of Mathematical Physics
Volume31
Issue number10
StatePublished - 1990
Externally publishedYes

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Wave packets
Klein-Gordon equation
Klein-Gordon Equation
Wave Packet
Dirac Equation
Dirac equation
wave packets
Synthesis
Group Velocity
Spin Models
synthesis
Maxwell's equations
Fermions
Wave equation
Scalar
Maxwell equations
Wave equations
Modeling
group velocity
Maxwell equation

ASJC Scopus subject areas

  • Organic Chemistry

Cite this

A novel approach to the synthesis of nondispersive wave packet solutions to the Klein-Gordon and Dirac equations. / Shaarawi, Amr M.; Besieris, Ioannis M.; Ziolkowski, Richard W.

In: Journal of Mathematical Physics, Vol. 31, No. 10, 1990, p. 2511-2519.

Research output: Contribution to journalArticle

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