Analysis of Characteristic of Free Particles: Relativistic Concept

A linear Hamiltonian in spatial derivative that satisfies Klein-Gordon equation was used starting from energy momentum relation for free particle was solved in agreement with the matrices and bearing in mind their suitability in terms of anticommutation relations in parallel with the definition of a...

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Bibliographic Details
Published in:Journal of modern physics 2012-10, Vol.3 (10), p.1394-1397
Main Authors: Ugwu, Emmanuel I., Onah, Daniel Ugadu, Oboma, D., Eke, V. O. C.
Format: Article
Language:English
Subjects:
Derivatives
Klein-Gordon equation
Plane waves
Representations
Schroedinger equation
Theorems
Wave functions
Wave packets
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Summary:A linear Hamiltonian in spatial derivative that satisfies Klein-Gordon equation was used starting from energy momentum relation for free particle was solved in agreement with the matrices and bearing in mind their suitability in terms of anticommutation relations in parallel with the definition of algebraic matrices whose hermicity is fulfilled by i + = i and + = and in turn linked up to explicit representation of the Dirac matrices. The wave packets of plane Dirac wave obtained as a superposition of plane wave yielding a localized wave function was normalized considering only positive energy of plane wave in which the expectation value with respect to the wave packet resulted from C2p/E+=(vgr) was found to agree with the Ehrenfest theorem in relation to Schrodinger theorem as it relates to true velocity of single particle. A comparison was made between the classical concept with Heisenberg representation from where the combined effect of the positive and negative energy components was considered.
ISSN:2153-1196
2153-120X
DOI:10.4236/jmp.2012.310176