Analysis of Characteristic of Free Particles: Relativistic Concept

Emmanuel I. Ugwu, Daniel Ugadu Onah, D. Oboma, V. O. C. Eke

Departments of Computer Science, Ebonyi State University, Abakaliki, Nigeria.
Departments of Industrial Physics, Ebonyi State University, Abakaliki, Nigeria.

DOI: 10.4236/jmp.2012.310176                

Abstract

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 2p/E>₊=<(v_gr)> 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.

Keywords

Hamiltonian; Klein-Gordon Equation; Wave Function; Dirac Matrices Wave Packet; Heisenberg Representation; Superposition; Energy; Group Velocity; Frequency

Conflicts of Interest

The authors declare no conflicts of interest.

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